 3.3.1: Sketch the graph of f for the indicated value of c or a.
 3.3.2: Sketch the graph of f for the indicated value of c or a.
 3.3.3: Sketch the graph of f for the indicated value of c or a.
 3.3.4: Sketch the graph of f for the indicated value of c or a.
 3.3.5: Use the intermediate value theorem to show that f has a zero betwee...
 3.3.6: Use the intermediate value theorem to show that f has a zero betwee...
 3.3.7: Use the intermediate value theorem to show that f has a zero betwee...
 3.3.8: Use the intermediate value theorem to show that f has a zero betwee...
 3.3.9: Use the intermediate value theorem to show that f has a zero betwee...
 3.3.10: Use the intermediate value theorem to show that f has a zero betwee...
 3.3.11: Match each graph with an equation. (A) (B) (C) (D) f(x) (x 1)(x 1)2...
 3.3.12: Match each graph with an equation. (A) (B) (C) (D)
 3.3.13: Use arrow notation to describe the end behavior of the function. Do...
 3.3.14: Use arrow notation to describe the end behavior of the function. Do...
 3.3.15: Find all values of x such that and all x such that , and sketch the...
 3.3.16: Find all values of x such that and all x such that , and sketch the...
 3.3.17: Find all values of x such that and all x such that , and sketch the...
 3.3.18: Find all values of x such that and all x such that , and sketch the...
 3.3.19: Find all values of x such that and all x such that , and sketch the...
 3.3.20: Find all values of x such that and all x such that , and sketch the...
 3.3.21: Find all values of x such that and all x such that , and sketch the...
 3.3.22: Find all values of x such that and all x such that , and sketch the...
 3.3.23: Find all values of x such that and all x such that , and sketch the...
 3.3.24: Find all values of x such that and all x such that , and sketch the...
 3.3.25: Find all values of x such that and all x such that , and sketch the...
 3.3.26: Find all values of x such that and all x such that , and sketch the...
 3.3.27: Find all values of x such that and all x such that , and sketch the...
 3.3.28: Find all values of x such that and all x such that , and sketch the...
 3.3.29: Find all values of x such that and all x such that , and sketch the...
 3.3.30: Find all values of x such that and all x such that , and sketch the...
 3.3.31: Sketch the graph of a polynomial given the sign diagram.
 3.3.32: Sketch the graph of a polynomial given the sign diagram.
 3.3.33: (a) Sketch a graph ofwhere .(b) What is the yintercept? (c) What i...
 3.3.34: (a) Sketch a graph ofwhere .(b) What is the yintercept? (c) What i...
 3.3.35: Let be a polynomial such that the coefficient of every odd power of...
 3.3.36: Let be a polynomial such that the coefficient of every even power o...
 3.3.37: If , find a number k such that the graph of f contains the point
 3.3.38: If , find a number k such that the graph of f contains the point
 3.3.39: If one zero of is 2, find two other zeros.
 3.3.40: If one zero of is , find two other zeros.
 3.3.41: A Legendre polynomial The thirddegree Legendre polynomial occurs i...
 3.3.42: A Chebyshev polynomial The fourthdegree Chebyshev polynomial occur...
 3.3.43: Constructing a box From a rectangular piece of cardboard having dim...
 3.3.44: Constructing a crate The frame for a shipping crate is to be constr...
 3.3.45: Determining temperatures A meteorologist determines that the temper...
 3.3.46: Deflections of diving boards A diver stands at the very end of a di...
 3.3.47: Deer population A herd of 100 deer is introduced onto a small islan...
 3.3.48: Deer population Refer to Exercise 47. It can be shown by means of c...
 3.3.49: (a) Construct a table containing the values of the fourthdegree pol...
 3.3.50: (a) Graph the cubic polynomialsandin the same coordinate plane, usi...
 3.3.51: (a) Graph each of the following cubic polynomials f in the viewing ...
 3.3.52: (a) Graph each of the following fourthdegree polynomials f in the ...
 3.3.53: Graph f, and estimate its zeros.
 3.3.54: Graph f, and estimate its zeros.
 3.3.55: Graph f, and estimate its zeros.
 3.3.56: Graph f, and estimate its zeros.
 3.3.57: Graph f, and estimate all values of x such that .
 3.3.58: Graph f, and estimate all values of x such that .
 3.3.59: Graph f, and estimate all values of x such that .
 3.3.60: Graph f, and estimate all values of x such that .
 3.3.61: Graph f and g on the same coordinate plane, and estimate the points...
 3.3.62: Graph f and g on the same coordinate plane, and estimate the points...
 3.3.63: Medicare recipients The function f given bywhere , approximates the...
 3.3.64: Head Start participants The function f given byapproximates the tot...
 3.3.1.1: Find the quotient and remainder if is divided by .
 3.3.1.2: Find the quotient and remainder if is divided by .
 3.3.1.3: Find the quotient and remainder if is divided by .
 3.3.1.4: Find the quotient and remainder if is divided by .
 3.3.1.5: Find the quotient and remainder if is divided by .
 3.3.1.6: Find the quotient and remainder if is divided by .
 3.3.1.7: Find the quotient and remainder if is divided by .
 3.3.1.8: Find the quotient and remainder if is divided by .
 3.3.1.9: Use the remainder theorem to find .
 3.3.1.10: Use the remainder theorem to find .
 3.3.1.11: Use the remainder theorem to find .
 3.3.1.12: Use the remainder theorem to find .
 3.3.1.13: Use the factor theorem to show that is a factor of .
 3.3.1.14: Use the factor theorem to show that is a factor of .
 3.3.1.15: Use the factor theorem to show that is a factor of .
 3.3.1.16: Use the factor theorem to show that is a factor of .
 3.3.1.17: Use the factor theorem to show that is a factor of .
 3.3.1.18: Use the factor theorem to show that is a factor of .
 3.3.1.19: Find a polynomial with leading coefficient 1 and having the given d...
 3.3.1.20: Find a polynomial with leading coefficient 1 and having the given d...
 3.3.1.21: Find a polynomial with leading coefficient 1 and having the given d...
 3.3.1.22: Find a polynomial with leading coefficient 1 and having the given d...
 3.3.1.23: Find a polynomial with leading coefficient 1 and having the given d...
 3.3.1.24: Find a polynomial with leading coefficient 1 and having the given d...
 3.3.1.25: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.26: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.27: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.28: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.29: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.30: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.31: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.32: Use synthetic division to find the quotient and remainder if the fi...
 3.3.1.33: Use synthetic division to find .
 3.3.1.34: Use synthetic division to find . fx x3 4x2 x
 3.3.1.35: Use synthetic division to find . fx 0.3x3 0.4x;
 3.3.1.36: Use synthetic division to find . f x 0.1x3 0.5x
 3.3.1.37: Use synthetic division to find . f x 27x5 2x2 1
 3.3.1.38: Use synthetic division to find . fx 8x5 3x2 7; c 1 2
 3.3.1.39: Use synthetic division to find . fx x2 3x 5; c 2 3
 3.3.1.40: Use synthetic division to find . fx x3 3x2 8; c 1 2
 3.3.1.41: Use synthetic division to show that c is a zero of . fx 3x4 8x3 2x2...
 3.3.1.42: Use synthetic division to show that c is a zero of . fx 4x3 9x2 8x ...
 3.3.1.43: Use synthetic division to show that c is a zero of . fx 4x3 6x2 8x ...
 3.3.1.44: Use synthetic division to show that c is a zero of .
 3.3.1.45: Find all values of k such that is divisible by the given linear pol...
 3.3.1.46: Find all values of k such that is divisible by the given linear pol...
 3.3.1.47: Show that x c is not a factor of for any real number c.
 3.3.1.48: Show that x c is not a factor of for any real number c.
 3.3.1.49: Find the remainder if the polynomialis divided by .
 3.3.1.50: Use the factor theorem to verify the statement. is a factor of for ...
 3.3.1.51: Use the factor theorem to verify the statement. is a factor of for ...
 3.3.1.52: Use the factor theorem to verify the statement. is a factor of for ...
 3.3.1.53: Let be a firstquadrant point on , and consider the vertical line s...
 3.3.1.54: Strength of a beam The strength of a rectangular beam is directly p...
 3.3.1.55: Parabolic arch An arch has the shape of the parabola . A rectangle ...
 3.3.1.56: Dimensions of a capsule An aspirin tablet in the shape of a right c...
 3.3.1.57: Use the graph of f to approximate the remainder if f is divided by ...
 3.3.1.58: Use the graph of f to approximate the remainder if f is divided by ...
 3.3.1.59: Use the graph of f to approximate all values of k such that is divi...
 3.3.1.60: Use the graph of f to approximate all values of k such that is divi...
 3.3.2.1: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.2: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.3: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.4: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.5: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.6: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.7: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.8: Find a polynomial f(x) of degree 3 that has the indicated zeros and...
 3.3.2.9: Find a polynomial of degree 4 with leading coefficient 1 such that ...
 3.3.2.10: Find a polynomial of degree 4 with leading coefficient 1 such that ...
 3.3.2.11: Find a polynomial of degree 6 such that 0 and 3 are both zeros of m...
 3.3.2.12: Find a polynomial of degree 7 such that and 2 are both zeros of mul...
 3.3.2.13: Find the thirddegree polynomial function whose graph is shown in t...
 3.3.2.14: Find the fourthdegree polynomial function whose graph is shown in ...
 3.3.2.15: Find the polynomial function of degree 3 whose graph is shown in th...
 3.3.2.16: Find the polynomial function of degree 3 whose graph is shown in th...
 3.3.2.17: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.18: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.19: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.20: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.21: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.22: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.23: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.24: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.25: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.26: Find the zeros of f(x), and state the multiplicity of each zero.
 3.3.2.27: Show that the number is a zero of f(x) of the given multiplicity, a...
 3.3.2.28: Show that the number is a zero of f(x) of the given multiplicity, a...
 3.3.2.29: Show that the number is a zero of f(x) of the given multiplicity, a...
 3.3.2.30: Show that the number is a zero of f(x) of the given multiplicity, a...
 3.3.2.31: Show that the number is a zero of f(x) of the given multiplicity, a...
 3.3.2.32: Show that the number is a zero of f(x) of the given multiplicity, a...
 3.3.2.33: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.34: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.35: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.36: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.37: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.38: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.39: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.40: Use Descartes rule of signs to determine the number of possible pos...
 3.3.2.41: Applying the first theorem on bounds for real zeros of polynomials,...
 3.3.2.42: Applying the first theorem on bounds for real zeros of polynomials,...
 3.3.2.43: Applying the first theorem on bounds for real zeros of polynomials,...
 3.3.2.44: Applying the first theorem on bounds for real zeros of polynomials,...
 3.3.2.45: Applying the first theorem on bounds for real zeros of polynomials,...
 3.3.2.46: Applying the first theorem on bounds for real zeros of polynomials,...
 3.3.2.47: Find a factored form for a polynomial function f that has minimal d...
 3.3.2.48: Find a factored form for a polynomial function f that has minimal d...
 3.3.2.49: (a) Find a factored form for a polynomial function f that has minim...
 3.3.2.50: (a) Find a factored form for a polynomial function f that has minim...
 3.3.2.51: The polynomial function f has only real zeros. Use the graph of f t...
 3.3.2.52: The polynomial function f has only real zeros. Use the graph of f t...
 3.3.2.53: Is there a polynomial of the given degree n whose graph contains th...
 3.3.2.54: Is there a polynomial of the given degree n whose graph contains th...
 3.3.2.55: Is there a polynomial of the given degree n whose graph contains th...
 3.3.2.56: Is there a polynomial of the given degree n whose graph contains th...
 3.3.2.57: Using limited data A scientist has limited data on the temperature ...
 3.3.2.58: Lagrange interpolation polynomial A polynomial of degree 3 with zer...
 3.3.2.59: Graph f for each value of n on the same coordinate plane, and descr...
 3.3.2.60: Graph f for each value of n on the same coordinate plane, and descr...
 3.3.2.61: Graph f, estimate all real zeros, and determine the multiplicity of...
 3.3.2.62: Graph f, estimate all real zeros, and determine the multiplicity of...
 3.3.2.63: Greenhouse effect Because of the combustion of fossil fuels, the co...
 3.3.2.64: Greenhouse effect The average increase in global surface temperatur...
 3.3.2.65: The average monthly temperatures in for two Canadian locations are ...
 3.3.2.66: The average monthly temperatures in for two Canadian locations are ...
 3.3.2.67: A solid wood sphere whose density is less than that of water will f...
 3.3.2.68: A solid wood sphere whose density is less than that of water will f...
 3.3.2.69: Refer to Exercises 67 and 68. Water has a kvalue of 1. If a sphere...
 3.3.3.1: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.2: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.3: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.4: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.5: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.6: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.7: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.8: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.9: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.10: A polynomial f(x) with real coefficients and leading coefficient 1 ...
 3.3.3.11: Show that the equation has no rational root.
 3.3.3.12: Show that the equation has no rational root.
 3.3.3.13: Show that the equation has no rational root.
 3.3.3.14: Show that the equation has no rational root.
 3.3.3.15: Show that the equation has no rational root.
 3.3.3.16: Show that the equation has no rational root.
 3.3.3.17: (a) List all possible rational zeros of f.(b) Use that list to dete...
 3.3.3.18: (a) List all possible rational zeros of f.(b) Use that list to dete...
 3.3.3.19: Find all solutions of the equation.
 3.3.3.20: Find all solutions of the equation.
 3.3.3.21: Find all solutions of the equation.
 3.3.3.22: Find all solutions of the equation.
 3.3.3.23: Find all solutions of the equation.
 3.3.3.24: Find all solutions of the equation.
 3.3.3.25: Find all solutions of the equation.
 3.3.3.26: Find all solutions of the equation.
 3.3.3.27: Find all solutions of the equation.
 3.3.3.28: Find all solutions of the equation.
 3.3.3.29: Find all solutions of the equation.
 3.3.3.30: Find all solutions of the equation.
 3.3.3.31: Find a factored form with integer coefficients of the polynomial f ...
 3.3.3.32: Find a factored form with integer coefficients of the polynomial f ...
 3.3.3.33: The polynomial function f has only real zeros. Use the graph of f t...
 3.3.3.34: The polynomial function f has only real zeros. Use the graph of f t...
 3.3.3.35: Does there exist a polynomial of degree 3 with real coefficients th...
 3.3.3.36: The polynomial has the complex number i as a zero; however, the con...
 3.3.3.37: If n is an odd positive integer, prove that a polynomial of degree ...
 3.3.3.38: If a polynomial of the formwhere each is an integer, has a rational...
 3.3.3.39: Constructing a box From a rectangular piece of cardboard having dim...
 3.3.3.40: Constructing a crate The frame for a shipping crate is to be constr...
 3.3.3.41: A right triangle has area and a hypotenuse that is 1 foot longer th...
 3.3.3.42: Constructing a storage tank A storage tank for propane gas is to be...
 3.3.3.43: Constructing a storage shelter A storage shelter is to be construct...
 3.3.3.44: Designing a tent A canvas camping tent is to be constructed in the ...
 3.3.3.45: Use a graph to determine the number of nonreal solutions of the equ...
 3.3.3.46: Use a graph to determine the number of nonreal solutions of the equ...
 3.3.3.47: Use a graph and synthetic division to find all solutions of the equ...
 3.3.3.48: Use a graph and synthetic division to find all solutions of the equ...
 3.3.3.49: Atmospheric density The density (in ) of Earths atmosphere at an al...
 3.3.3.50: Earths density Earths density (in ) h meters underneath the surface...
 3.3.4.1: (a) Sketch the graph of f. (b) Find the domain D and range R of f. ...
 3.3.4.2: (a) Sketch the graph of f. (b) Find the domain D and range R of f. ...
 3.3.4.3: Use the graph to complete the statements. (a) As x , f(x) ____. (b)...
 3.3.4.4: Use the graph to complete the statements. (a) As x , f(x) ____. (b)...
 3.3.4.5: Use arrow notation to describe the end behavior of the function.
 3.3.4.6: Use arrow notation to describe the end behavior of the function.
 3.3.4.7: Identify any vertical asymptotes, horizontal asymptotes, and holes....
 3.3.4.8: Identify any vertical asymptotes, horizontal asymptotes, and holes....
 3.3.4.9: All asymptotes, intercepts, and holes of a rational function f are ...
 3.3.4.10: All asymptotes, intercepts, and holes of a rational function f are ...
 3.3.4.11: Sketch the graph of f.
 3.3.4.12: Sketch the graph of f.
 3.3.4.13: Sketch the graph of f.
 3.3.4.14: Sketch the graph of f.
 3.3.4.15: Sketch the graph of f.
 3.3.4.16: Sketch the graph of f.
 3.3.4.17: Sketch the graph of f.
 3.3.4.18: Sketch the graph of f.
 3.3.4.19: Sketch the graph of f.
 3.3.4.20: Sketch the graph of f.
 3.3.4.21: Sketch the graph of f.
 3.3.4.22: Sketch the graph of f.
 3.3.4.23: Sketch the graph of f.
 3.3.4.24: Sketch the graph of f.
 3.3.4.25: Sketch the graph of f.
 3.3.4.26: Sketch the graph of f.
 3.3.4.27: Sketch the graph of f.
 3.3.4.28: Sketch the graph of f.
 3.3.4.29: Sketch the graph of f.
 3.3.4.30: Sketch the graph of f.
 3.3.4.31: Sketch the graph of f.
 3.3.4.32: Sketch the graph of f.
 3.3.4.33: Sketch the graph of f.
 3.3.4.34: Sketch the graph of f.
 3.3.4.35: Sketch the graph of f.
 3.3.4.36: Sketch the graph of f.
 3.3.4.37: Find the oblique asymptote, and sketch the graph of f.
 3.3.4.38: Find the oblique asymptote, and sketch the graph of f. fx 2x2 x 3 x 2
 3.3.4.39: Find the oblique asymptote, and sketch the graph of f.
 3.3.4.40: Find the oblique asymptote, and sketch the graph of f. fx x3 1 x2 9
 3.3.4.41: Find the curvilinear asymptote.
 3.3.4.42: Find the curvilinear asymptote. fx x5 3x3 x2 1 x2 3
 3.3.4.43: Simplify f(x), and sketch the graph of f.
 3.3.4.44: Simplify f(x), and sketch the graph of f.
 3.3.4.45: Simplify f(x), and sketch the graph of f.
 3.3.4.46: Simplify f(x), and sketch the graph of f.
 3.3.4.47: Simplify f(x), and sketch the graph of f.
 3.3.4.48: Simplify f(x), and sketch the graph of f.
 3.3.4.49: Simplify f(x), and sketch the graph of f.
 3.3.4.50: Simplify f(x), and sketch the graph of f.
 3.3.4.51: Find an equation of a rational function f that satisfies the given ...
 3.3.4.52: Find an equation of a rational function f that satisfies the given ...
 3.3.4.53: Find an equation of a rational function f that satisfies the given ...
 3.3.4.54: Find an equation of a rational function f that satisfies the given ...
 3.3.4.55: A container for radioactive waste A cylindrical container for stori...
 3.3.4.56: Drug dosage Youngs rule is a formula that is used to modify adult d...
 3.3.4.57: Salt concentration Salt water of concentration 0.1 pound of salt pe...
 3.3.4.58: Amount of rainfall The total number of inches of rain during a stor...
 3.3.4.59: Salmon propagation For a particular salmon population, the relation...
 3.3.4.60: Population density The population density D (in ) in a large city i...
 3.3.4.61: Graph f, and find equations of the vertical asymptotes.fx 20x2 80x ...
 3.3.4.62: Graph f, and find equations of the vertical asymptotes.fx 15x2 60x ...
 3.3.4.63: Graph f, and find equations of the vertical asymptotes.
 3.3.4.64: Graph f, and find equations of the vertical asymptotes.fx x2 9.01
 3.3.4.65: Let be the polynomial.(a) Describe the graph of .(b) Describe the g...
 3.3.4.66: Refer to Exercise 65. (a) Describe the graph of .(b) Describe the g...
 3.3.4.67: Grade point average (GPA) (a) A student has finished 48 credit hour...
 3.3.5.1: Express the statement as a formula that involves the given variable...
 3.3.5.2: Express the statement as a formula that involves the given variable...
 3.3.5.3: Express the statement as a formula that involves the given variable...
 3.3.5.4: Express the statement as a formula that involves the given variable...
 3.3.5.5: Express the statement as a formula that involves the given variable...
 3.3.5.6: Express the statement as a formula that involves the given variable...
 3.3.5.7: Express the statement as a formula that involves the given variable...
 3.3.5.8: Express the statement as a formula that involves the given variable...
 3.3.5.9: Express the statement as a formula that involves the given variable...
 3.3.5.10: Express the statement as a formula that involves the given variable...
 3.3.5.11: Express the statement as a formula that involves the given variable...
 3.3.5.12: Express the statement as a formula that involves the given variable...
 3.3.5.13: Express the statement as a formula that involves the given variable...
 3.3.5.14: Express the statement as a formula that involves the given variable...
 3.3.5.15: Express the statement as a formula that involves the given variable...
 3.3.5.16: Express the statement as a formula that involves the given variable...
 3.3.5.17: Liquid pressure The pressure P acting at a point in a liquid is dir...
 3.3.5.18: Hookes law Hookes law states that the force F required to stretch a...
 3.3.5.19: Electrical resistance The electrical resistance R of a wire varies ...
 3.3.5.20: Intensity of illumination The intensity of illumination I from a so...
 3.3.5.21: Period of a pendulum The period P of a simple pendulumthat is, the ...
 3.3.5.22: Dimensions of a human limb A circular cylinder is sometimes used in...
 3.3.5.23: Period of a planet Keplers third law states that the period T of a ...
 3.3.5.24: Range of a projectile It is known from physics that the range R of ...
 3.3.5.25: Automobile skid marks The speed V at which an automobile was travel...
 3.3.5.26: Coulombs law Coulombs law in electrical theory states that the forc...
 3.3.5.27: Threshold weight Threshold weight W is defined to be that weight be...
 3.3.5.28: The ideal gas law The ideal gas law states that the volume V that a...
 3.3.5.29: Poiseuilles law Poiseuilles law states that the blood flow rate F (...
 3.3.5.30: Trout population Suppose 200 trout are caught, tagged, and released...
 3.3.5.31: Radioactive decay of radon gas When uranium disintegrates into lead...
 3.3.5.32: Radon concentration Refer to Exercise 31. Find the change in the ra...
 3.3.5.33: Density at a point A thin flat plate is situated in an xyplane such...
 3.3.5.34: Temperature at a point A flat metal plate is positioned in an xypl...
 3.3.5.35: Examine the expression for the given set of data points of the form...
 3.3.5.36: Examine the expression for the given set of data points of the form...
 3.3.5.37: Examine the expression for the given set of data points of the form...
 3.3.5.38: Examine the expression for the given set of data points of the form...
 3.3.5.39: Stopping distances Refer to Exercise 86 in Section 2.4. The distanc...
 3.3.6.1: Find all values of x such that and all x such that , and sketch the...
 3.3.6.2: Find all values of x such that and all x such that , and sketch the...
 3.3.6.3: Find all values of x such that and all x such that , and sketch the...
 3.3.6.4: Find all values of x such that and all x such that , and sketch the...
 3.3.6.5: Find all values of x such that and all x such that , and sketch the...
 3.3.6.6: Find all values of x such that and all x such that , and sketch the...
 3.3.6.7: If , use the intermediate value theorem for polynomial functions to...
 3.3.6.8: Prove that the equation has a solution between 0 and 1.
 3.3.6.9: Find the quotient and remainder if f(x) is divided by p(x). fx 3x5 ...
 3.3.6.10: Find the quotient and remainder if f(x) is divided by p(x). fx 4x3 ...
 3.3.6.11: If , use the remainder theorem to find .
 3.3.6.12: Use the factor theorem to show that is a factor of
 3.3.6.13: Use synthetic division to find the quotient and remainder if f(x) i...
 3.3.6.14: Use synthetic division to find the quotient and remainder if f(x) i...
 3.3.6.15: A polynomial with real coefficients has the indicated zero(s) and d...
 3.3.6.16: A polynomial with real coefficients has the indicated zero(s) and d...
 3.3.6.17: Find a polynomial of degree 7 with leading coefficient 1 such that ...
 3.3.6.18: Show that 2 is a zero of multiplicity 3 of the polynomial , and exp...
 3.3.6.19: Find the zeros of f(x), and state the multiplicity of each zero. fx...
 3.3.6.20: Find the zeros of f(x), and state the multiplicity of each zero. fx...
 3.3.6.21: (a) Use Descartes rule of signs to determine the number of possible...
 3.3.6.22: (a) Use Descartes rule of signs to determine the number of possible...
 3.3.6.23: Show that has no real zero.
 3.3.6.24: Find all solutions of the equation. x4 9x3 31x2 49x 30 0
 3.3.6.25: Find all solutions of the equation. 16 x3 20x2 8x 3 0
 3.3.6.26: Find all solutions of the equation. x4 x3 7x2 x 6 0
 3.3.6.27: Find an equation for the sixthdegree polynomial f shown in the fig...
 3.3.6.28: Find an equation for the sixthdegree polynomial f shown in the fig...
 3.3.6.29: Identify any vertical asymptotes, horizontal asymptotes,intercepts,...
 3.3.6.31: Sketch the graph of f.
 3.3.6.32: Sketch the graph of f.
 3.3.6.33: Sketch the graph of f.
 3.3.6.34: Sketch the graph of f.
 3.3.6.35: Sketch the graph of f.
 3.3.6.36: Sketch the graph of f.
 3.3.6.37: Sketch the graph of f.
 3.3.6.38: Sketch the graph of f.
 3.3.6.39: Sketch the graph of f.
 3.3.6.40: Find an equation of a rational function f that satisfies the given ...
 3.3.6.41: Suppose y is directly proportional to the cube root of x and invers...
 3.3.6.42: Suppose y is inversely proportional to the square of x. Sketch a gr...
 3.3.6.43: Deflection of a beam A horizontal beam l feet long is supported at ...
 3.3.6.44: Elastic cylinder A rectangle made of elastic material is to be made...
 3.3.6.45: Determining temperatures A meteorologist determines that the temper...
 3.3.6.46: Deer propagation A herd of 100 deer is introduced onto a small isla...
 3.3.6.47: Threshold response curve In biochemistry, the general threshold res...
 3.3.6.48: Oil spill cleanup The cost of cleaning up x percent of an oil spil...
 3.3.6.49: Telephone calls In a certain county, the average number of telephon...
 3.3.6.50: Power of a wind rotor The power P generated by a wind rotor is dire...
 3.3.7.1: Compare the domain, range, number of xintercepts, and general shap...
 3.3.7.2: When using synthetic division, could you use a complex number c rat...
 3.3.7.3: Discuss how synthetic division can be used to help find the quotien...
 3.3.7.4: Draw (by hand) a graph of a polynomial function of degree 3 that ha...
 3.3.7.5: How many different points do you need to specify a polynomial of de...
 3.3.7.6: Prove the theorem on conjugate pair zeros of a polynomial. (Hint: F...
 3.3.7.7: Give an example of a rational function that has a common factor in ...
 3.3.7.8: (a) Can the graph of (where ) cross its horizontal asymptote? If ye...
 3.3.7.9: Gambling survival formula An empirical formula for the bankroll B (...
 3.3.7.10: Multiply three consecutive integers together and then add the secon...
 3.3.7.11: Personal tax rate Assume the total amount of state tax paid consist...
 3.3.7.12: NFL passer rating The National Football League ranks its passers by...
 3.3.8.1: Sketch the graph of . What is the yintercept?
 3.3.8.2: The graph of the function f has xintercepts at x 0, 1, and 2. Writ...
 3.3.8.3: Use the intermediate value theorem to show that has a zero between ...
 3.3.8.4: What is the solution to f(x) 0, where and a 0 b c?
 3.3.8.5: Suppose the number N(t) of a type of animal after t years is given ...
 3.3.8.6: The figure shows a graph of and . What would happen to the graphs i...
 3.3.8.7: Use the factor theorem to show that x 2 is a factor of .
 3.3.8.8: Given that the graph of passes through the point (4, b), find the v...
 3.3.8.9: Find all values of k such that is divisible by x 1.
 3.3.8.10: A polynomial f has 3 as a zero of multiplicity 1, has 1 as a zero o...
 3.3.8.11: A thirddegree polynomial f passes through the following points: (2...
 3.3.8.12: Is it possible to have a polynomial f of degree 3 that has zeros 0,...
 3.3.8.13: Explain why could be a rational root of
 3.3.8.14: The function has possible rational roots 1,,,,2,,3,,,,5,,6,,10,15,,...
 3.3.8.15: The function intersects its horizontal asymptote. Find that point (...
 3.3.8.16: Find the x and ycoordinates of the hole of .
 3.3.8.17: Sketch the graph of . Label the x and yintercepts, horizontal and...
 3.3.8.18: Find an equation of a rational function f that has an xintercept a...
 3.3.8.19: z is directly proportional to the square of x and inversely proport...
Solutions for Chapter 3: POLYNOMIAL AND RATIONAL FUNCTIONS
Full solutions for Precalculus: Functions and Graphs  12th Edition
ISBN: 9780840068576
Solutions for Chapter 3: POLYNOMIAL AND RATIONAL FUNCTIONS
Get Full SolutionsChapter 3: POLYNOMIAL AND RATIONAL FUNCTIONS includes 429 full stepbystep solutions. Since 429 problems in chapter 3: POLYNOMIAL AND RATIONAL FUNCTIONS have been answered, more than 19266 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus: Functions and Graphs, edition: 12. Precalculus: Functions and Graphs was written by and is associated to the ISBN: 9780840068576. This expansive textbook survival guide covers the following chapters and their solutions.

Addition property of inequality
If u < v , then u + w < v + w

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Augmented matrix
A matrix that represents a system of equations.

Census
An observational study that gathers data from an entire population

Complements or complementary angles
Two angles of positive measure whose sum is 90°

End behavior
The behavior of a graph of a function as.

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Exponent
See nth power of a.

Ordered pair
A pair of real numbers (x, y), p. 12.

Phase shift
See Sinusoid.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Range of a function
The set of all output values corresponding to elements in the domain.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Solve a system
To find all solutions of a system.

Statistic
A number that measures a quantitative variable for a sample from a population.

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.