 2.2.2.1: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.1: In Exercises 1 to 6, plot the image of the given point with respect...
 2.2.6.1: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.1: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.1: In Exercises 1 and 2, plot the points whose coordinates are given o...
 2.2.7.1: Use a graphing calculator for this Exercise Set. In Exercises 1 to ...
 2.2.4.1: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.1: In Exercises 1 and 2, find the distance between the points whose co...
 2.2.2.2: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.2: In Exercises 1 to 6, plot the image of the given point with respect...
 2.2.6.2: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.2: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.2: In Exercises 1 and 2, plot the points whose coordinates are given o...
 2.2.7.2: Use a graphing calculator for this Exercise Set. In Exercises 1 to ...
 2.2.4.2: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.2: In Exercises 1 and 2, find the distance between the points whose co...
 2.2.2.3: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.3: In Exercises 1 to 6, plot the image of the given point with respect...
 2.2.6.3: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.3: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.3: College Debt The following graph shows the average debt, in constan...
 2.2.7.3: Use a graphing calculator for this Exercise Set. In Exercises 1 to ...
 2.2.4.3: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.3: In Exercises 3 and 4, find the midpoint of the line segment with th...
 2.2.2.4: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.4: In Exercises 1 to 6, plot the image of the given point with respect...
 2.2.6.4: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.4: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.4: Computer Games The graph below shows the results of market research...
 2.2.7.4: Use a graphing calculator for this Exercise Set. In Exercises 1 to ...
 2.2.4.4: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.4: In Exercises 3 and 4, find the midpoint of the line segment with th...
 2.2.2.5: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.5: In Exercises 1 to 6, plot the image of the given point with respect...
 2.2.6.5: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.5: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.5: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.5: In Exercises 5 and 6, determine for which scatter diagram, A or B, ...
 2.2.4.5: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.5: In Exercises 5 to 8, graph each equation by plotting points. 2x  y...
 2.2.2.6: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.6: In Exercises 1 to 6, plot the image of the given point with respect...
 2.2.6.6: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.6: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.6: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.6: In Exercises 5 and 6, determine for which scatter diagram, A or B, ...
 2.2.4.6: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.6: In Exercises 5 to 8, graph each equation by plotting points. 2x2 + ...
 2.2.2.7: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.7: In Exercises 7 and 8, sketch a graph that is symmetric to the given...
 2.2.6.7: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.7: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.7: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.7: In Exercises 7 to 12, find the linear regression equation for the g...
 2.2.4.7: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.7: In Exercises 5 to 8, graph each equation by plotting points. y = x ...
 2.2.2.8: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.8: In Exercises 7 and 8, sketch a graph that is symmetric to the given...
 2.2.6.8: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.8: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.8: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.8: In Exercises 7 to 12, find the linear regression equation for the g...
 2.2.4.8: In Exercises 1 to 8, match each graph in a. through h. with the pro...
 2.8: In Exercises 5 to 8, graph each equation by plotting points. y =  2x
 2.2.2.9: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.9: In Exercises 9 and 10, sketch a graph that is symmetric to the give...
 2.2.6.9: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.9: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.9: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.9: In Exercises 7 to 12, find the linear regression equation for the g...
 2.2.4.9: In Exercises 9 to 18, use the method of completing the square to fi...
 2.9: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.2.2.10: In Exercises 1 to 10, state whether the equation defines y as a fun...
 2.2.5.10: In Exercises 9 and 10, sketch a graph that is symmetric to the give...
 2.2.6.10: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.10: In Exercises 1 to 10, find the slope of the line that passes throug...
 2.2.1.10: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.10: In Exercises 7 to 12, find the linear regression equation for the g...
 2.2.4.10: In Exercises 9 to 18, use the method of completing the square to fi...
 2.10: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.2.2.11: In Exercises 11 to 16, state whether the set of ordered pairs (x, y...
 2.2.5.11: In Exercises 11 and 12, sketch a graph that is symmetric to the giv...
 2.2.6.11: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.11: In Exercises 11 to 14, find the slope of the line that passes throu...
 2.2.1.11: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.11: In Exercises 7 to 12, find the linear regression equation for the g...
 2.2.4.11: In Exercises 9 to 18, use the method of completing the square to fi...
 2.11: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.2.2.12: In Exercises 11 to 16, state whether the set of ordered pairs (x, y...
 2.2.5.12: In Exercises 11 and 12, sketch a graph that is symmetric to the giv...
 2.2.6.12: In Exercises 1 to 12, use the given functions f and g to find f g f...
 2.2.3.12: In Exercises 11 to 14, find the slope of the line that passes throu...
 2.2.1.12: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.12: In Exercises 7 to 12, find the linear regression equation for the g...
 2.2.4.12: In Exercises 9 to 18, use the method of completing the square to fi...
 2.12: In Exercises 9 to 12, find the x and yintercepts of the graph of ...
 2.2.2.13: In Exercises 11 to 16, state whether the set of ordered pairs (x, y...
 2.2.5.13: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.13: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.13: In Exercises 11 to 14, find the slope of the line that passes throu...
 2.2.1.13: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.13: In Exercises 13 to 16, find a quadratic model for the given data. 5...
 2.2.4.13: In Exercises 9 to 18, use the method of completing the square to fi...
 2.13: In Exercises 13 and 14, determine the center and radius of the circ...
 2.2.2.14: In Exercises 11 to 16, state whether the set of ordered pairs (x, y...
 2.2.5.14: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.14: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.14: In Exercises 11 to 14, find the slope of the line that passes throu...
 2.2.1.14: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.14: In Exercises 13 to 16, find a quadratic model for the given data. 5...
 2.2.4.14: In Exercises 9 to 18, use the method of completing the square to fi...
 2.14: In Exercises 13 and 14, determine the center and radius of the circ...
 2.2.2.15: In Exercises 11 to 16, state whether the set of ordered pairs (x, y...
 2.2.5.15: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.15: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.15: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.15: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.15: In Exercises 13 to 16, find a quadratic model for the given data. 5...
 2.2.4.15: In Exercises 9 to 18, use the method of completing the square to fi...
 2.15: In Exercises 15 and 16, find the equation in standard form of the c...
 2.2.2.16: In Exercises 11 to 16, state whether the set of ordered pairs (x, y...
 2.2.5.16: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.16: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.16: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.16: In Exercises 5 to 16, find the distance between the points whose co...
 2.2.7.16: In Exercises 13 to 16, find a quadratic model for the given data. 5...
 2.2.4.16: In Exercises 9 to 18, use the method of completing the square to fi...
 2.16: In Exercises 15 and 16, find the equation in standard form of the c...
 2.2.2.17: In Exercises 17 to 24, evaluate each function. Given f(x) = 3x  1,...
 2.2.5.17: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.17: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.17: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.17: Find all points on the xaxis that are 10 units from the point (4, ...
 2.2.7.17: Archeology The data below show the length of the humerus and the to...
 2.2.4.17: In Exercises 9 to 18, use the method of completing the square to fi...
 2.17: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.2.2.18: In Exercises 17 to 24, evaluate each function. Given g(x) = 2x2 + 3...
 2.2.5.18: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.18: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.18: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.18: Find all points on the yaxis that are 12 units from the point (5, ...
 2.2.7.18: Sports The data in the table below show the distance, in feet, a ba...
 2.2.4.18: In Exercises 9 to 18, use the method of completing the square to fi...
 2.18: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.2.2.19: In Exercises 17 to 24, evaluate each function. Given A(w) = 2w2 + 5...
 2.2.5.19: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.19: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.19: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.19: In Exercises 19 to 24, find the midpoint of the line segment with t...
 2.2.7.19: Sports The table below shows the number of strokes per minute that ...
 2.2.4.19: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.19: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.2.2.20: In Exercises 17 to 24, evaluate each function. Given J(t) = 3t2  t...
 2.2.5.20: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.20: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.20: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.20: In Exercises 19 to 24, find the midpoint of the line segment with t...
 2.2.7.20: Biology A medical researcher wants to determine the effect of pH (a...
 2.2.4.20: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.20: In Exercises 17 to 20, determine whether the equation defines y as ...
 2.2.2.21: In Exercises 17 to 24, evaluate each function. Given f(x) = 1 x , f...
 2.2.5.21: In Exercises 13 to 21, determine whether the graph of each equation...
 2.2.6.21: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.21: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.21: In Exercises 19 to 24, find the midpoint of the line segment with t...
 2.2.7.21: Health The body mass index (BMI) of a person is a measure of the pe...
 2.2.4.21: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.21: If f(x) = 3x2 + 4x  5, find a. f(1) b. f(3) c. f(t) d. f(x + h) e...
 2.2.2.22: In Exercises 17 to 24, evaluate each function. Given T(x) = 5, find...
 2.2.5.22: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.22: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.22: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.22: In Exercises 19 to 24, find the midpoint of the line segment with t...
 2.2.7.22: Health The BMI (see Exercise 21) of a person depends on height, as ...
 2.2.4.22: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.22: If g(x) = 264  x2, find a. g(3) b. g(5) c. g(8) d. g(x) e. 2g(t)...
 2.23: Let f be a piecewisedefined function given by f(x) = e3x + 2, x 6 ...
 2.2.2.23: In Exercises 17 to 24, evaluate each function. Given s(x) = x x, fi...
 2.2.5.23: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.23: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.23: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.23: In Exercises 19 to 24, find the midpoint of the line segment with t...
 2.2.7.23: Industrial Engineering Permanentmagnet directcurrent motors are u...
 2.2.4.23: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.24: Let f be a piecewisedefined function given by f(x) = cx + 4, x 6 ...
 2.2.2.24: In Exercises 17 to 24, evaluate each function. Given r(x) = xx + 4,...
 2.2.5.24: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.24: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.24: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.24: In Exercises 19 to 24, find the midpoint of the line segment with t...
 2.2.7.24: Health Sciences The average remaining lifetime for men in the Unite...
 2.2.4.24: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.25: In Exercises 25 to 28, determine the domain of the function represe...
 2.2.2.25: In Exercises 25 and 26, evaluate each piecewisedefined function fo...
 2.2.5.25: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.25: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.25: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.25: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.25: Health Sciences The average remaining lifetime for women in the Uni...
 2.2.4.25: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.26: In Exercises 25 to 28, determine the domain of the function represe...
 2.2.2.26: In Exercises 25 and 26, evaluate each piecewisedefined function fo...
 2.2.5.26: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.26: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.26: In Exercises 15 to 26, graph y as a function of x by finding the sl...
 2.2.1.26: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.26: Biology The table below gives the body lengths, in centimeters, and...
 2.2.4.26: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.27: In Exercises 25 to 28, determine the domain of the function represe...
 2.2.2.27: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.27: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.27: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.27: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.27: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.27: Health The table below shows the number of calories burned in 1 hou...
 2.2.4.27: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.28: In Exercises 25 to 28, determine the domain of the function represe...
 2.2.2.28: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.28: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.28: In Exercises 13 to 28, evaluate the indicated function, where f (x)...
 2.2.3.28: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.28: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.28: Traffic Safety A traffic safety institute measured the braking dist...
 2.2.4.28: In Exercises 19 to 28, use the vertex formula to determine the vert...
 2.29: Find the values of a in the domain of f(x) = x2 + 2x  4 for which ...
 2.2.2.29: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.29: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.29: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.29: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.29: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.29: Biology The survival of certain larvae after hatching depends on th...
 2.2.4.29: Find the range of f(x) = x2  2x  1. Determine the values of x in ...
 2.30: Find the value of a in the domain of f(x) = 4x + 1 for which f(a) = 2
 2.2.2.30: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.30: In Exercises 22 to 30, determine whether the graph of each equation...
 2.2.6.30: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.30: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.30: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.30: Meteorology The temperature at various times on a summer day at a r...
 2.2.4.30: Find the range of f(x) = x2  6x  2 . Determine the values of x i...
 2.31: In Exercises 31 and 32, graph the given equation. f(x) = x  1  1
 2.2.2.31: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.31: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.31: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.31: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.31: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.31: Automotive Engineering The fuel efficiency, in miles per gallon, fo...
 2.2.4.31: Find the range of f(x) = 2x2 + 5x  1. Determine the values of x i...
 2.32: In Exercises 31 and 32, graph the given equation. f(x) = 4  1x
 2.2.2.32: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.32: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.32: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.32: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.32: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.32: Biology The data in the following table show the oxygen consumption...
 2.2.4.32: Find the range of f(x) = 2x2 + 6x  5. Determine the values of x in...
 2.33: In Exercises 33 and 34, find the zero or zeros of the given functio...
 2.2.2.33: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.33: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.33: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.33: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.33: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.33: Physics Galileo (15641642) studied acceleration due to gravity by a...
 2.2.4.33: In Exercises 33 to 36, find the real zeros of f and the xintercept...
 2.34: In Exercises 33 and 34, find the zero or zeros of the given functio...
 2.2.2.34: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.34: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.34: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.34: In Exercises 27 to 34, graph each equation by first writing the equ...
 2.2.1.34: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.7.34: Astronomy In 1929, Edwin Hubble published a paper that revolutioniz...
 2.2.4.34: In Exercises 33 to 36, find the real zeros of f and the xintercept...
 2.35: In Exercises 35 and 36, find each function value. Let g(x) = 2x. a....
 2.2.2.35: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.35: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.35: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.35: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.35: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.4.35: In Exercises 33 to 36, find the real zeros of f and the xintercept...
 2.36: In Exercises 35 and 36, find each function value. Let f(x) = 1  x....
 2.2.2.36: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.36: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.36: In Exercises 29 to 36, find the difference quotient of the given fu...
 2.2.3.36: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.36: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.4.36: In Exercises 33 to 36, find the real zeros of f and the xintercept...
 2.37: In Exercises 37 to 40, find the slope of the line between the point...
 2.2.2.37: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.37: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.37: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.37: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.37: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.4.37: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.38: In Exercises 37 to 40, find the slope of the line between the point...
 2.2.2.38: In Exercises 27 to 38, determine the domain of the function represe...
 2.2.5.38: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.38: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.38: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.38: In Exercises 25 to 38, graph each equation by plotting points that ...
 2.2.4.38: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.39: In Exercises 37 to 40, find the slope of the line between the point...
 2.2.2.39: In Exercises 39 to 50, graph each function. f(x) = 3x  4
 2.2.5.39: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.39: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.39: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.39: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.39: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.40: In Exercises 37 to 40, find the slope of the line between the point...
 2.2.2.40: In Exercises 39 to 50, graph each function. f(x) = 2  1
 2.2.5.40: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.40: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.40: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.40: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.40: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.2.4.41: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.41: Graph f(x) =  34 x + 2 using the slope and yintercept.
 2.2.2.41: In Exercises 39 to 50, graph each function. g(x) = x2  1
 2.2.5.41: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.41: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.41: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.41: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.42: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.42: Graph f(x) = 2  x using the slope and yintercept.
 2.2.2.42: In Exercises 39 to 50, graph each function. g(x) = 3  x2
 2.2.5.42: In Exercises 31 to 42, graph the given equation. Label each interce...
 2.2.6.42: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.42: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.42: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.43: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.43: Graph 3x  4y = 8.
 2.2.2.43: In Exercises 39 to 50, graph each function. f(x) = 1x + 4
 2.2.5.43: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.43: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.43: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.43: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.44: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.44: Graph 2x + 3y = 9
 2.2.2.44: In Exercises 39 to 50, graph each function. h(x) = 15  x
 2.2.5.44: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.44: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.44: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.44: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.45: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.45: Find the equation of the line that passes through the point with co...
 2.2.2.45: In Exercises 39 to 50, graph each function. f(x) = x  2
 2.2.5.45: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.45: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.45: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.45: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.46: In Exercises 37 to 46, find the maximum or minimum value of the fun...
 2.46: Find the equation of the line that passes through the point with co...
 2.2.2.46: In Exercises 39 to 50, graph each function. h(x) = 3  x
 2.2.5.46: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.46: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.46: In Exercises 35 to 46, find the equation of the indicated line. Wri...
 2.2.1.46: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.47: Astronaut Training To prepare astronauts for the experience of zero...
 2.47: Find the equation of the line that passes through the points with c...
 2.2.2.47: In Exercises 39 to 50, graph each function. 6 x 613L
 2.2.5.47: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.47: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.47: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.47: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.48: Soccer Ball Kick The height , in meters, above the ground of a cert...
 2.48: Find the equation of the line that passes through the points with c...
 2.2.2.48: In Exercises 39 to 50, graph each function. M(x) = x+ 2 0 x 4
 2.2.5.48: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.48: In Exercises 37 to 48, find (g f )(x) and (f g )(x) for the given f...
 2.2.3.48: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.48: In Exercises 39 to 48, find the x and yintercepts of the graph of...
 2.2.4.49: Height of an Arch The height of an arch is given by h(x) =  3 64 x...
 2.49: Find the slopeintercept form of the equation of the line that passe...
 2.2.2.49: In Exercises 39 to 50, graph each function. N(x) = int(x) 3 x 3
 2.2.5.49: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.49: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.49: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.49: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.50: Geometry The sum of the length l and the width w of a rectangular a...
 2.50: Find the slopeintercept form of the equation of the line that passe...
 2.2.2.50: In Exercises 39 to 50, graph each function. P(x) = int(x) + x 0 x 4
 2.2.5.50: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.50: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.50: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.50: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.51: Rectangular Enclosure A veterinarian uses 600 feet of chainlink fen...
 2.51: Find the slopeintercept form of the equation of the line that passe...
 2.2.2.51: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.51: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.51: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.51: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.51: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.52: Rectangular Enclosure A farmer uses 1200 feet of fence to enclose a...
 2.52: Find the slopeintercept form of the equation of the line that passe...
 2.2.2.52: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.52: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.52: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.52: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.52: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.53: Temperature Fluctuations The temperature , in degrees Fahrenheit, d...
 2.53: Sports The speed of a professional golfers swing and the speed of t...
 2.2.2.53: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.53: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.53: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.53: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.53: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.54: Larvae Survival Soon after insect larvae are hatched, they must beg...
 2.54: Food Science Newer heating elements allow an oven to reach a normal...
 2.2.2.54: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.54: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.54: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.54: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.54: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.55: Sports When a softball player swings a bat, the amount of energy , ...
 2.55: In Exercises 55 to 60, use the method of completing the square to w...
 2.2.2.55: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.55: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.55: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.55: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.55: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.56: Geology In June 2001, Mt. Etna in Sicily, Italy, erupted, sending v...
 2.56: In Exercises 55 to 60, use the method of completing the square to w...
 2.2.2.56: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.56: In Exercises 43 to 56, determine whether the given function is an e...
 2.2.6.56: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.56: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.56: In Exercises 49 to 56, determine the center and radius of the circl...
 2.2.4.57: Sports For a serve to be legal in tennis, the ball must be at least...
 2.57: In Exercises 55 to 60, use the method of completing the square to w...
 2.2.2.57: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.57: Use the graph of to sketch the graph of a. y = f(x) + 3 b. y = f(x ...
 2.2.6.57: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.57: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.57: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.58: Sports A pitcher releases a baseball 6 feet above the ground at a s...
 2.58: In Exercises 55 to 60, use the method of completing the square to w...
 2.2.2.58: In Exercises 51 to 58, find the value or values of a in the domain ...
 2.2.5.58: Use the graph of to sketch the graph of a. y = g(x)  2 b. y = g(x ...
 2.2.6.58: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.58: In Exercises 47 to 58, find the equation of the line, in slopeinter...
 2.2.1.58: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.59: Automotive Engineering The fuel efficiency for a certain midsize ca...
 2.59: In Exercises 55 to 60, use the method of completing the square to w...
 2.2.2.59: In Exercises 59 to 66, find the zeros of f. f(x) = 3x  6
 2.2.5.59: Use the graph of to sketch the graph of a. y = f(x + 2) b. y = f(x)...
 2.2.6.59: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.59: Find the value of a in the domain of f(x) = 2x + 3 for which f(a) =...
 2.2.1.59: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.60: Sports Some football fields are built in a parabolic mound shape so...
 2.60: In Exercises 55 to 60, use the method of completing the square to w...
 2.2.2.60: In Exercises 59 to 66, find the zeros of f. f(x) = 6 + 2x
 2.2.5.60: Use the graph of to sketch the graph of a. y = g(x  1) b. y = g(x)...
 2.2.6.60: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.60: Find the value of a in the domain of f(x) = 4  3x for which f(a) = 7.
 2.2.1.60: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.61: Business In Exercises 61 and 62, determine the number of units x th...
 2.61: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.2.2.61: In Exercises 59 to 66, find the zeros of f. f(x) = 5x + 2
 2.2.5.61: Use the graph of f to sketch a graph of a. y = f(x  2) + 1 b. y = ...
 2.2.6.61: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.61: Find the value of a in the domain of f(x) = 1  4x for which f(a) = 3.
 2.2.1.61: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.62: Business In Exercises 61 and 62, determine the number of units x th...
 2.62: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.2.2.62: In Exercises 59 to 66, find the zeros of f. f(x) = 8  6x
 2.2.5.62: Use the graph of g to sketch a graph of a. y = g(x + 3) + 2 b. y = ...
 2.2.6.62: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.62: Find the value of a in the domain of f(x) = 2x3+ 2 for which f(a) = 4.
 2.2.1.62: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.63: Business In Exercises 63 and 64, determine the number of units x th...
 2.63: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.2.2.63: In Exercises 59 to 66, find the zeros of f. f(x) = x + 4x  21 2  4
 2.2.5.63: Let be a function such that f(2) = 5, f(0) = 2, and f(1) = 0. Giv...
 2.2.6.63: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.63: In Exercises 63 to 66, find the zero of f. Verify that the solution...
 2.2.1.63: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.64: Business In Exercises 63 and 64, determine the number of units x th...
 2.64: In Exercises 61 to 64, find the vertex of the graph of the quadrati...
 2.2.2.64: In Exercises 59 to 66, find the zeros of f. f(x) = x2 f(x) = x + 4x...
 2.2.5.64: Let be a function such that g(3) = 1, g(1) = 3, and g(4) = 2. Gi...
 2.2.6.64: In Exercises 49 to 64, evaluate each composite function, where f (x...
 2.2.3.64: In Exercises 63 to 66, find the zero of f. Verify that the solution...
 2.2.1.64: In Exercises 57 to 64, find an equation of a circle that satisfies ...
 2.2.4.65: Business In Exercises 65 and 66, determine the profit function for ...
 2.65: In Exercises 65 and 66, find the requested value. The maximum value...
 2.2.2.65: In Exercises 59 to 66, find the zeros of f. f(x) = x + 3x  5 2  5...
 2.2.5.65: Use the graph of to sketch the graph of a. y = f(x) b. y = f(x) x...
 2.2.6.65: In Exercises 65 to 68, show that (f g)(x) = (g f )(x). f(x) = 2x + ...
 2.2.3.65: In Exercises 63 to 66, find the zero of f. Verify that the solution...
 2.2.1.65: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.66: Business In Exercises 65 and 66, determine the profit function for ...
 2.66: In Exercises 65 and 66, find the requested value. The minimum value...
 2.2.2.66: In Exercises 59 to 66, find the zeros of f. f(x) = 2x2 f(x) = x + 3...
 2.2.5.66: Use the graph of to sketch the graph of a. y = g(x) b. y = g(x) 4...
 2.2.6.66: In Exercises 65 to 68, show that (f g)(x) = (g f )(x). f(x) = 4x  ...
 2.2.3.66: In Exercises 63 to 66, find the zero of f. Verify that the solution...
 2.2.1.66: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.67: Tour Cost A charter bus company has determined that the cost, in do...
 2.67: Height of a Ball A ball is thrown vertically upward with an initial...
 2.2.2.67: In Exercises 67 to 72, use the floor function to write and then eva...
 2.2.5.67: Let be a function such that f(1) = 3 and f(2) = 4. Give the coord...
 2.2.6.67: In Exercises 65 to 68, show that (f g)(x) = (g f )(x). f(x) = 6xx ...
 2.2.3.67: Oceanography The graph below shows the relationship between the spe...
 2.2.1.67: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.68: Delivery Cost An air freight company has determined that the cost, ...
 2.68: Delivery Cost A freight company has determined that its cost, in do...
 2.2.2.68: In Exercises 67 to 72, use the floor function to write and then eva...
 2.2.5.68: Let be a function such that g(4) = 5 and g(3) = 2. Give the coord...
 2.2.6.68: In Exercises 65 to 68, show that (f g)(x) = (g f )(x). f(x) = 5xx +...
 2.2.3.68: Computer Science The following graph shows the relationship between...
 2.2.1.68: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.69: Projectile If the initial velocity of a projectile is 128 feet per ...
 2.69: Agriculture A farmer wishes to enclose a rectangular region borderi...
 2.2.2.69: In Exercises 67 to 72, use the floor function to write and then eva...
 2.2.5.69: Use the graph of to sketch the graph of a. y = F(x) b. y = F(x). ...
 2.2.6.69: In Exercises 69 to 72, show that (gf)(x) = x and (gf )(x) = x. f(x)...
 2.2.3.69: Automotive Technology The following table shows the U.S. Environmen...
 2.2.1.69: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.70: Projectile The height in feet of a projectile with an initial veloc...
 2.70: In Exercises 70 and 71, sketch a graph that is symmetric to the giv...
 2.2.2.70: In Exercises 67 to 72, use the floor function to write and then eva...
 2.2.5.70: Use the graph of to sketch the graph of a. y = E(x) b. y = E(x). ...
 2.2.6.70: In Exercises 69 to 72, show that (gf)(x) = x and (gf )(x) = x. f(x)...
 2.2.3.70: Consumer Credit The amount of revolving consumer credit (such as cr...
 2.2.1.70: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.71: Fire Management The height of a stream of water from the nozzle of ...
 2.71: In Exercises 70 and 71, sketch a graph that is symmetric to the giv...
 2.2.2.71: In Exercises 67 to 72, use the floor function to write and then eva...
 2.2.5.71: Use the graph of to sketch the graph of m x y 2 4 2 y =  1 2 m m(x...
 2.2.6.71: In Exercises 69 to 72, show that (gf)(x) = x and (gf )(x) = x. f(x)...
 2.2.3.71: Labor Market According to the Bureau of Labor Statistics (BLS), the...
 2.2.1.71: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.72: Astronaut Training A weightless environment can be created in an ai...
 2.72: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.72: In Exercises 67 to 72, use the floor function to write and then eva...
 2.2.5.72: Use the graph of nt o sketch the graph of y = 12 n n(x) + 1. y10864...
 2.2.6.72: In Exercises 69 to 72, show that (gf)(x) = x and (gf )(x) = x. f(x)...
 2.2.3.72: Pottery A piece of pottery is removed from a kiln and allowed to co...
 2.2.1.72: In Exercises 65 to 72, find the center and radius of the graph of t...
 2.2.4.73: Norman Window A Norman window has the shape of a rectangle surmount...
 2.73: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.73: FirstClass Mail In 2009, the cost to mail a firstclass letter was...
 2.2.5.73: Use the graph of to sketch the graph of a. y = f(2x) b. y = f 13. y...
 2.2.6.73: Water Tank A water tank has the shape of a right circular cone with...
 2.2.3.73: Lumber Industry The number of boardfeet (bf) that can be obtained ...
 2.2.1.73: In Exercises 73 to 76, find an equation of the circle described. Wr...
 2.2.4.74: Golden Gate Bridge The suspension cables of the main span of the Go...
 2.74: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.74: Income Tax The amount of federal income tax a single person owed in...
 2.2.5.74: Use the graph of to sketch the graph of a. y = g(2x) b. y = ga x 86...
 2.2.6.74: Scaling a Rectangle Rework Example 7 of this section with the scali...
 2.2.3.74: Ecology The rate at which water evaporates from a certain reservoir...
 2.2.1.74: In Exercises 73 to 76, find an equation of the circle described. Wr...
 2.75: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.75: Vertical Line Test Use the vertical line test to determine which of...
 2.2.5.75: Use the graph of to sketch the graph of a. y = h(2x) b. y = ha yh2 ...
 2.2.6.75: Towing a Boat A boat is towed by a rope that runs through a pulley ...
 2.2.3.75: Cycling Speeds Michelle and Amanda start from the same place on a c...
 2.2.1.75: In Exercises 73 to 76, find an equation of the circle described. Wr...
 2.76: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.76: Vertical Line Test Use the vertical line test to determine which of...
 2.2.5.76: Use the graph of y = j(x) to sketch the graph of a. y = j(2x) b. y ...
 2.2.6.76: Shadow Position The light from a lamppost casts a shadow from a bal...
 2.2.3.76: Temperature The following graph shows the temperature, in degrees F...
 2.2.1.76: In Exercises 73 to 76, find an equation of the circle described. Wr...
 2.77: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.77: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.77: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.6.77: Conversion Functions The function F(x) = x12 converts x inches to f...
 2.2.3.77: Health The following table shows the average remaining lifetime, by...
 2.2.1.77: In Exercises 77 to 80, find the other endpoint of the line segment ...
 2.78: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.78: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.78: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.6.78: Conversion Functions The function F(x) = 3x converts x yards to fee...
 2.2.3.78: Health The following table shows the average remaining lifetime, by...
 2.2.1.78: In Exercises 77 to 80, find the other endpoint of the line segment ...
 2.79: In Exercises 72 to 79, determine whether the graph of each equation...
 2.2.2.79: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.79: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.6.79: Concentration of a Medication The concentration C(t) (in milligrams...
 2.2.3.79: Business In Exercises 79 to 82, determine the profit function for t...
 2.2.1.79: In Exercises 77 to 80, find the other endpoint of the line segment ...
 2.2.1.80: In Exercises 77 to 80, find the other endpoint of the line segment ...
 2.80: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.2.2.80: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.80: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.6.80: Ball Rolling on a Ramp The distance traveled by a ball rolling down...
 2.2.3.80: Business In Exercises 79 to 82, determine the profit function for t...
 2.2.1.81: Find a formula for the set of all points (x, y) for which the dista...
 2.81: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.2.2.81: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.81: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.3.81: Business In Exercises 79 to 82, determine the profit function for t...
 2.2.1.82: Find a formula for the set of all points (x, y) for which the dista...
 2.82: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.2.2.82: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.82: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.3.82: Business In Exercises 79 to 82, determine the profit function for t...
 2.83: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.2.2.83: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.83: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.3.83: Marginal Cost In business, marginal cost is a phrase used to repres...
 2.84: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.2.2.84: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.84: In Exercises 77 to 84, use a graphing utility. On the same coordina...
 2.2.3.84: Marginal Revenue In business, marginal revenue is a phrase used to ...
 2.85: In Exercises 80 to 85, sketch the graph of g. a. Find the domain an...
 2.2.2.85: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.85: Graph V(x) = cx, 0 x 6, for each value of c. a. c = 1 b. c = c. c =...
 2.2.3.85: BreakEven Point for a Rental Truck A rental company purchases a tr...
 2.86: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.2.2.86: In Exercises 77 to 86, use the indicated graph to identify the inte...
 2.2.5.86: Graph W(x) = cx cx 0, 0 x 6, for each value of c. a. c = 1 b. c = ...
 2.2.3.86: BreakEven Point for a Publisher A magazine company had a profit of...
 2.87: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.2.2.87: Horizontal Line Test Use the horizontal line test to determine whic...
 2.2.3.87: Point of Impact A rock attached to a string is whirled horizontally...
 2.88: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.2.2.88: Horizontal Line Test Use the horizontal line test to determine whic...
 2.2.3.88: Point of Impact A rock attached to a string is whirled horizontally...
 2.89: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.2.2.89: Geometry A rectangle has a length of feet and a perimeter of 50 fee...
 2.2.3.89: Slope of a Secant Line The graph of is shown below with and Q(2 + h...
 2.90: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.2.2.90: Length of a Shadow A child 4 feet tall is standing near a street la...
 2.2.3.90: Slope of a Secant Line The graph of is shown below with and as two ...
 2.91: In Exercises 86 to 91, use the graph of f shown below to sketch a g...
 2.2.2.91: Depreciation A bus was purchased for $80,000. Assuming that the bus...
 2.2.3.91: Verify that the slope of the line passing through (x, x2) and (x + ...
 2.92: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.2.2.92: Depreciation A boat was purchased for $44,000. Assuming that the bo...
 2.2.3.92: Verify that the slope of the line passing through (x, 4x2) and (x +...
 2.93: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.2.2.93: Cost, Revenue, and Profit A manufacturer produces a product at a co...
 2.2.3.93: Determine whether there is a point on the graph of the equation suc...
 2.94: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.2.2.94: Volume of a Box An open box is to be made from a square piece of ca...
 2.2.3.94: Determine whether there is a point on the graph of the equation suc...
 2.95: In Exercises 92 to 95, use the graph of f shown below to sketch a g...
 2.2.2.95: Height of an Inscribed Cylinder A cone has an altitude of 15 centim...
 2.96: Let f(x) = x g(x) = 3x + 1 2 + x  2 and g(x) = 3x + 1. Find each o...
 2.2.2.96: Volume of Water Water is flowing into a conical drinking cup with a...
 2.97: If f(x) = 4x2  3x  1, find the difference quotient f(x + h)  f(x)h
 2.2.2.97: Distance from a Balloon For the first minute of flight, a hot air b...
 2.98: If g(x) = x3  x, find the difference quotient g(x + h)  g(x)h
 2.2.2.98: Time for an Athlete An athlete swims from point to point at a rate ...
 2.99: Ball Rolling on a Ramp The distance traveled by a ball rolling down...
 2.2.2.99: Distance Between Ships At noon, Ship A is 45 miles due south of Shi...
 2.100: If f(x) = x g(x) = x  8 2 + 4x and g(x) = x  8, find a. f g)(3) b...
 2.2.2.100: Area A rectangle is bounded by the x and yaxes and the graph of a...
 2.101: If f(x) = 2x g(x)2 + 7 and g(x) = x  1, find a. ( f g)(5) b. (g f...
 2.2.2.101: Area A piece of wire 20 centimeters long is cut at a point x centim...
 2.102: Sports A soccer coach examined the relationship between the speed, ...
 2.2.2.102: Area A triangle is bounded by the x and yaxes and must pass throu...
 2.103: Physics The rate at which water will escape from the bottom of a ru...
 2.2.2.103: Length Two guy wires are attached to utility poles that are 40 feet...
 2.2.2.104: Sales vs. Price A business finds that the number of feet of pipe it...
 2.2.2.105: Model Yield The yield of apples per tree is related to the amount o...
 2.2.2.106: Model Cost A manufacturer finds that the cost in dollars of produci...
 2.2.2.107: If f(x) = x2  x  5and f(c) = 1, find c.
 2.2.2.108: If and g(x) = 2x g(c) = 4, find c.
 2.2.2.109: Determine whether 1 is in the range of f(x) = x  1x + 1
 2.2.2.110: Determine whether 0 is in the range of g(x) = 1x  3
 2.2.2.111: In Exercises 111 to 116, use a graphing utility. Graph f(x) = 4.7 ...
 2.2.2.112: In Exercises 111 to 116, use a graphing utility. Graph f(x) = 4 x ...
 2.2.2.113: In Exercises 111 to 116, use a graphing utility. Graph: f(x) = x2 ...
 2.2.2.114: In Exercises 111 to 116, use a graphing utility. Graph: f(x) = x2 ...
 2.2.2.115: In Exercises 111 to 116, use a graphing utility. Graph: f(x) = x2 ...
 2.2.2.116: In Exercises 111 to 116, use a graphing utility. Graph: f(x) = x2 ...
 2.2.2.117: A fixed point of a function is a number a such that In Exercises 11...
 2.2.2.118: A fixed point of a function is a number a such that In Exercises 11...
 2.2.2.119: Day of the Week A formula known as Zellers Congruence makes use of ...
Solutions for Chapter 2: Functions and Graphs
Full solutions for College Algebra  7th Edition
ISBN: 9781439048610
Solutions for Chapter 2: Functions and Graphs
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9781439048610. This textbook survival guide was created for the textbook: College Algebra, edition: 7. Chapter 2: Functions and Graphs includes 672 full stepbystep solutions. Since 672 problems in chapter 2: Functions and Graphs have been answered, more than 40337 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.