In Exercises 4756, (a) use a graphing utility to graph the function and visually

Fill in the blanks. The graph of a function is the collection of ________ ________ such that is in the domain of

Fill in the blanks. The ________ ________ ________ is used to determine whether the graph of an equation is a function of in terms of

Fill in the blanks. The ________ of a function are the values of for which

Fill in the blanks. A function is ________ on an interval if, for any and in the interval, implies

Fill in the blanks. A function value is a relative ________ of if there exists an interval containing such that implies

Fill in the blanks. The ________ ________ ________ ________ between any two points and is the slope of the line through the two points, and this line is called the ________ line.

Fill in the blanks. A function is ________ if, for each in the domain of

Fill in the blanks. A function is ________ if its graph is symmetric with respect to the -axis.

In Exercises 9 12, use the graph of the function to find the domain and range of

In Exercises 9 12, use the graph of the function to find the domain and range of

In Exercises 9 12, use the graph of the function to find the domain and range of

In Exercises 9 12, use the graph of the function to find the domain and range of

In Exercises 1316, use the graph of the function to find the domain and range of and the indicated function values.

In Exercises 1316, use the graph of the function to find the domain and range of and the indicated function values.

In Exercises 1316, use the graph of the function to find the domain and range of and the indicated function values.

In Exercises 1316, use the graph of the function to find the domain and range of and the indicated function values.

In Exercises 1722, use the Vertical Line Test to determine whether is a function of To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

In Exercises 1722, use the Vertical Line Test to determine whether is a function of To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

In Exercises 1722, use the Vertical Line Test to determine whether is a function of To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

In Exercises 1722, use the Vertical Line Test to determine whether is a function of To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

In Exercises 1722, use the Vertical Line Test to determine whether is a function of To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

In Exercises 1722, use the Vertical Line Test to determine whether is a function of To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 2332, find the zeros of the function algebraically

In Exercises 3338, (a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically.

In Exercises 3338, (a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically.

In Exercises 3338, (a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically.

In Exercises 3338, (a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically.

In Exercises 3338, (a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically.

In Exercises 3338, (a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 39 46, determine the intervals over which the function is increasing, decreasing, or constant.

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 4756, (a) use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whether the function is increasing, decreasing, or constant over the intervals you identified in part (a).

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 5766, use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 6774, graph the function and determine the interval(s) for which

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 75 82, find the average rate of change of the function from

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 8390, determine whether the function is even, odd, or neither. Then describe the symmetry.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 91100, sketch a graph of the function and determine whether it is even, odd, or neither. Verify your answers algebraically.

In Exercises 101104, write the height of the rectangle as a function of x

In Exercises 101104, write the height of the rectangle as a function of x

In Exercises 101104, write the height of the rectangle as a function of x

In Exercises 101104, write the height of the rectangle as a function of x

In Exercises 105108, write the length of the rectangle as a function of y

In Exercises 105108, write the length of the rectangle as a function of y

In Exercises 105108, write the length of the rectangle as a function of y

In Exercises 105108, write the length of the rectangle as a function of y

ELECTRONICS The number of lumens (time rate of flow of light) from a fluorescent lamp can be approximated by the model where is the wattage of the lamp. (a) Use a graphing utility to graph the function. (b) Use the graph from part (a) to estimate the wattage necessary to obtain 2000 lumens.

DATA ANALYSIS: TEMPERATURE The table shows the temperatures (in degrees Fahrenheit) in a certain city over a 24-hour period. Let represent the time of day, where corresponds to 6 A.M. A model that represents these data is given by (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. (e) Could this model be used to predict the temperatures in the city during the next 24-hour period? Why or why not?

COORDINATE AXIS SCALE Each function described below models the specified data for the years 1998 through 2008, with corresponding to 1998. Estimate a reasonable scale for the vertical axis (e.g., hundreds, thousands, millions, etc.) of the graph and justify your answer. (There are many correct answers.) (a) represents the average salary of college professors. (b) represents the U.S. population. (c) represents the percent of the civilian work force that is unemployed.

GEOMETRY Corners of equal size are cut from a square with sides of length 8 meters (see figure). (a) Write the area of the resulting figure as a function of Determine the domain of the function. (b) Use a graphing utility to graph the area function over its domain. Use the graph to find the range of the function. (c) Identify the figure that would result if were chosen to be the maximum value in the domain of the function. What would be the length of each side of the figure?

ENROLLMENT RATE The enrollment rates of children in preschool in the United States from 1970 through 2005 can be approximated by the model where represents the year, with corresponding to 1970. (Source: U.S. Census Bureau) (a) Use a graphing utility to graph the model. (b) Find the average rate of change of the model from 1970 through 2005. Interpret your answer in the context of the problem.

VEHICLE TECHNOLOGY SALES The estimated revenues (in millions of dollars) from sales of in-vehicle technologies in the United States from 2003 through 2008 can be approximated by the model where represents the year, with corresponding to 2003. (Source: Consumer Electronics Association) (a) Use a graphing utility to graph the model. (b) Find the average rate of change of the model from 2003 through 2008. Interpret your answer in the context of the problem. PHYSICS In Exercises 115120, (a) use the position equation to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from to (d) describe the slope of the secant line through and (e) find the equation of the secant line through and and (f) graph the secant line in the same viewing window as your position function.

An object is thrown upward from a height of 6 feet at a velocity of 64 feet per second.

An object is thrown upward from a height of 6.5 feet at a velocity of 72 feet per second.

An object is thrown upward from ground level at a velocity of 120 feet per second.

An object is thrown upward from ground level at a velocity of 96 feet per second.

An object is dropped from a height of 120 feet.

An object is dropped from a height of 80 feet.

A function with a square root cannot have a domain that is the set of real numbers.

It is possible for an odd function to have the interval as its domain.

If is an even function, determine whether is even, odd, or neither. Explain. (a) (b) (c) (d)

THINK ABOUT IT Does the graph in Exercise 19 represent as a function of Explain.

THINK ABOUT IT In Exercises 125130, find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is (a) even and (b) odd.

THINK ABOUT IT In Exercises 125130, find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is (a) even and (b) odd.

THINK ABOUT IT In Exercises 125130, find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is (a) even and (b) odd.

THINK ABOUT IT In Exercises 125130, find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is (a) even and (b) odd.

THINK ABOUT IT In Exercises 125130, find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is (a) even and (b) odd.

THINK ABOUT IT In Exercises 125130, find the coordinates of a second point on the graph of a function if the given point is on the graph and the function is (a) even and (b) odd.

WRITING Use a graphing utility to graph each function. Write a paragraph describing any similarities and differences you observe among the graphs. (a) (b) (c) (d) (e) (f )

CONJECTURE Use the results of Exercise 131 to make a conjecture about the graphs of and Use a graphing utility to graph the functions and compare the results with your conjecture.

Use the information in Example 7 to find the average speed of the car from to seconds. Explain why the result is less than the value obtained in part (b) of Example 7.

Graph each of the functions with a graphing utility. Determine whether the function is even, odd, or neither. What do you notice about the equations of functions that are odd? What do you notice about the equations of functions that are even? Can you describe a way to identify a function as odd or even by inspecting the equation? Can you describe a way to identify a function as neither odd nor even by inspecting the equation?

WRITING Write a short paragraph describing three different functions that represent the behaviors of quantities between 1998 and 2009. Describe one quantity that decreased during this time, one that increased, and one that was constant. Present your results graphically.

CAPSTONE Use the graph of the function to answer (a)(e). (a) Find the domain and range of (b) Find the zero(s) of (c) Determine the intervals over which is increasing, decreasing, or constant. (d) Approximate any relative minimum or relative maximum values of (e) Is f even, odd, or neither?