Explanation Given: The rational function is given below, s ( x ) = 4 x − 8 ( x − 4 ) ( x + 1 ) Calculation: The rational function is given below, s ( x ) = 4 x − 8 ( x − 4 ) ( x + 1 ) The x- intercepts are the zeros of the numerator, 4 x − 8 = 0 4 x = 8 x = 8 4 x = 2 The x- intercept of the given function is 2. Substitute 0 for x in rational function s ( x ) = 4 x − 8 ( x − 4 ) ( x + 1 ) , to find the y- intercept of the function s ( x ) , s ( 0 ) = 4 ( 0 ) − 8 ( ( 0 ) − 4 ) ( ( 0 ) + 1 ) = − 8 ( − 4 ) ( 1 ) = − 8 − 4 = 2 So, the y- intercept of given rational function is 2. There are two asymptotes: Vertical asymptote and Horizontal asymptote. The vertical asymptotes occur where the dominator is zero and where the function is undefined. The zeros of dominator of the rational function s ( x ) is, ( x − 4 ) ( x + 1 ) = 0 Simplify the above expression, x − 4 = 0 x = 4 And x + 1 = 0 x = − 1 So, the vertical asymptotes are x = − 1 and x = 4 . In the above equation numerator degree is 1 and denominator degree is 2. The numerator degree is less than the denominator degree, therefore the horizontal asymptote is y = 0 . Thus, the x- intercept of the rational function s ( x ) = 4 x − 8 ( x − 4 ) ( x + 1 ) is 2 and y- intercept is 2. The vertical asymptotes are x = − 1 , x = 4 and horizontal asymptote is y = 0 . The given rational function is, s ( x ) = 4 x − 8 ( x − 4 ) ( x + 1 ) (1) The behavior near the vertical asymptotes is determined by the sign of y for x values near the vertical asymptotes x = − 1 . For x → − 1 − , the close value to left of − 1 is − 1.1 . Substitute − 1.1 for x and y for s ( x ) in equation (1), to check the sign of y to the left of x = − 1 , y = 4 ( − 1.1 ) − 8 ( ( − 1.1 ) − 4 ) ( ( − 1.1 ) + 1 ) The sign is, y = ( − ) ( − ) ( − ) Which is negative, so y → − ∞ as x → − 1 − . For x → − 1 + , the close value to right of − 1 is − 0.9 . Substitute − 0.9 for x and y for s ( x ) in equation (1), to check the sign of y to the right of x = − 1 , y = 4 ( − 0.9 ) − 8 ( ( − 0.9 ) − 4 ) ( ( − 0.9 ) + 1 ) The sign is, y = ( − ) ( − ) ( + ) Which is positive, so y → ∞ as x → − 1 +

7th Edition

ISBN: 9781305761049

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage

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Chapter 3.6, Problem 49E

To determine

To evaluate: The intercepts and asymptotes of the rational function s(x)=4x−8(x−4)(x+1) , sketch the graph of this function and state the domain and range. Prove the answer by graphing device.

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Chapter 3.6, Problem 48E

Chapter 3.6, Problem 50E

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Chapter 3 Solutions

Precalculus

Ch. 3.1 - To put the quadratic function f(x)=ax2+bx+c in...Ch. 3.1 - The quadratic function f(x) = a(x - h)2 + k is in...Ch. 3.1 - The graph of f(x) = 3(x - 2)2 - 6 is a parabola...Ch. 3.1 - The graph of f(x) = -3(x - 2)2 - 6 is a parabola...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Maximum and Minimum Values A quadratic function f...Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Maximum and Minimum Values A quadratic function f...Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Maximum and Minimum Values A quadratic function f...Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Formula for Maximum and Minimum Values Find the...Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Formula for Maximum and Minimum Values Find the...Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Finding Quadratic Functions Find a function f...Ch. 3.1 - Finding Quadratic Functions Find a function f...Ch. 3.1 - Maximum of a Fourth-Degree Polynomial Find the...Ch. 3.1 - Maximum of a Fourth-Degree Polynomial Find the...Ch. 3.1 - Height of a Ball If a ball is thrown directly...Ch. 3.1 - Path of a Ball A ball is thrown across a playing...Ch. 3.1 - Revenue A manufacturer finds that the revenue...Ch. 3.1 - Sales A soft-drink vendor at a popular beach...Ch. 3.1 - Advertising The effectiveness of a television...Ch. 3.1 - Pharmaceuticals When a certain drug is taken...Ch. 3.1 - Agriculture The number of apples produced by each...Ch. 3.1 - Agriculture At a certain vineyard it is found that...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Fencing a Horse Corral Carol has 2400 ft of...Ch. 3.1 - Making a Rain Gutter A rain gutter is formed by...Ch. 3.1 - Stadium Revenue A baseball team plays in a stadium...Ch. 3.1 - Maximizing Profit A community bird-watching...Ch. 3.1 - Prob. 67E Ch. 3.2 - Only one of the following graphs could be the...Ch. 3.2 - Describe the end behavior of each polynomial. (a)...Ch. 3.2 - If c is a zero of the polynomial P, then (a) P(c)...Ch. 3.2 - Which of the following statements couldnt possibly...Ch. 3.2 - Transformations of Monomials Sketch the graph of...Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - Graphing Factored Polynomials Sketch the graph of...Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Graphing Polynomials Factor the polynomial and use...Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.2 - End Behavior Determine the end behavior of P....Ch. 3.2 - End Behavior Determine the end behavior of P....Ch. 3.2 - Prob. 49E Ch. 3.2 - End Behavior Determine the end behavior of P....Ch. 3.2 - Prob. 51E Ch. 3.2 - Prob. 52E Ch. 3.2 - Prob. 53E Ch. 3.2 - Local Extrema The graph of a polynomial function...Ch. 3.2 - Prob. 55E Ch. 3.2 - Local Extrema Graph the polynomial in the given...Ch. 3.2 - Prob. 57E Ch. 3.2 - Prob. 58E Ch. 3.2 - Prob. 59E Ch. 3.2 - Local Extrema Graph the polynomial in the given...Ch. 3.2 - Prob. 61E Ch. 3.2 - Prob. 62E Ch. 3.2 - Prob. 63E Ch. 3.2 - Prob. 64E Ch. 3.2 - Prob. 65E Ch. 3.2 - Prob. 66E Ch. 3.2 - Prob. 67E Ch. 3.2 - Prob. 68E Ch. 3.2 - Prob. 69E Ch. 3.2 - Prob. 70E Ch. 3.2 - Prob. 71E Ch. 3.2 - Prob. 72E Ch. 3.2 - Prob. 73E Ch. 3.2 - Prob. 74E Ch. 3.2 - Prob. 75E Ch. 3.2 - Families of Polynomials Graph the family of...Ch. 3.2 - Prob. 77E Ch. 3.2 - Prob. 78E Ch. 3.2 - Prob. 79E Ch. 3.2 - Power Functions Portions of the graphs of y = x2,...Ch. 3.2 - Prob. 81E Ch. 3.2 - Prob. 82E Ch. 3.2 - Prob. 83E Ch. 3.2 - Local Extrema These exercises involve local maxima...Ch. 3.2 - Local Extrema These exercises involve local maxima...Ch. 3.2 - Prob. 86E Ch. 3.2 - Market Research A market analyst working for a...Ch. 3.2 - Population Change The rabbit population on a small...Ch. 3.2 - Volume of a Box An open box is to be constructed...Ch. 3.2 - Volume of a Box A cardboard box has a square base,...Ch. 3.2 - Prob. 91E Ch. 3.2 - DISCUSS DISCOVER: Possible Number of Local...Ch. 3.3 - If we divide the polynomial P by the factor x c...Ch. 3.3 - (a) If we divide the polynomial P(x) by the factor...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Prob. 47E Ch. 3.3 - Remainder Theorem Use synthetic division and the...Ch. 3.3 - Prob. 49E Ch. 3.3 - Prob. 50E Ch. 3.3 - Prob. 51E Ch. 3.3 - Prob. 52E Ch. 3.3 - Prob. 53E Ch. 3.3 - Factor Theorem Use the Factor Theorem to show that...Ch. 3.3 - Factor Theorem Use the Factor Theorem to show that...Ch. 3.3 - Prob. 56E Ch. 3.3 - Prob. 57E Ch. 3.3 - Prob. 58E Ch. 3.3 - Prob. 59E Ch. 3.3 - Prob. 60E Ch. 3.3 - Factor Theorem Show that the given value(s) of c...Ch. 3.3 - Prob. 62E Ch. 3.3 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.3 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.3 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.3 - Prob. 66E Ch. 3.3 - Polynomials with Specified Zeros Find a polynomial...Ch. 3.3 - Polynomials with Specified Zeros Find a polynomial...Ch. 3.3 - Polynomials with Specified Zeros Find a polynomial...Ch. 3.3 - Prob. 70E Ch. 3.3 - Finding a Polynomial from a Graph Find the...Ch. 3.3 - Finding a Polynomial from a Graph Find the...Ch. 3.3 - Finding a Polynomial from a Graph Find the...Ch. 3.3 - Prob. 74E Ch. 3.3 - DISCUSS: Impossible Division? Suppose you were...Ch. 3.3 - Prob. 76E Ch. 3.4 - If the polynomial function...Ch. 3.4 - Using Descartes Rule of Signs, we can tell that...Ch. 3.4 - True or False? If c is a real zero of the...Ch. 3.4 - True or False? If a is an upper bound for the real...Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Possible Rational Zeros List all possible rational...Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Possible Rational Zeros A polynomial function P...Ch. 3.4 - Possible Rational Zeros A polynomial function P...Ch. 3.4 - Prob. 15E Ch. 3.4 - Integer Zeros All the real zeros of the given...Ch. 3.4 - Prob. 17E Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Integer Zeros All the real zeros of the given...Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Prob. 24E Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Real Zeros of a Polynomial Find all the real zeros...Ch. 3.4 - Real Zeros of a Polynomial Find all the real zeros...Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.4 - Prob. 51E Ch. 3.4 - Prob. 52E Ch. 3.4 - Prob. 53E Ch. 3.4 - Prob. 54E Ch. 3.4 - Prob. 55E Ch. 3.4 - Prob. 56E Ch. 3.4 - Prob. 57E Ch. 3.4 - Prob. 58E Ch. 3.4 - Prob. 59E Ch. 3.4 - Prob. 60E Ch. 3.4 - Prob. 61E Ch. 3.4 - Prob. 62E Ch. 3.4 - Descartes Rule of Signs Use Descartes Rule of...Ch. 3.4 - Descartes Rule of Signs Use Descartes Rule of...Ch. 3.4 - Prob. 65E Ch. 3.4 - Prob. 66E Ch. 3.4 - Prob. 67E Ch. 3.4 - Prob. 68E Ch. 3.4 - Prob. 69E Ch. 3.4 - Prob. 70E Ch. 3.4 - Prob. 71E Ch. 3.4 - Prob. 72E Ch. 3.4 - Prob. 73E Ch. 3.4 - Prob. 74E Ch. 3.4 - Prob. 75E Ch. 3.4 - Prob. 76E Ch. 3.4 - Upper and Lower Bounds Find integers that are...Ch. 3.4 - Prob. 78E Ch. 3.4 - Prob. 79E Ch. 3.4 - Prob. 80E Ch. 3.4 - Prob. 81E Ch. 3.4 - Prob. 82E Ch. 3.4 - Prob. 83E Ch. 3.4 - Prob. 84E Ch. 3.4 - Prob. 85E Ch. 3.4 - Prob. 86E Ch. 3.4 - Prob. 87E Ch. 3.4 - Prob. 88E Ch. 3.4 - Prob. 89E Ch. 3.4 - Polynomials With No Rational Zeros Show that the...Ch. 3.4 - Prob. 91E Ch. 3.4 - Prob. 92E Ch. 3.4 - Prob. 93E Ch. 3.4 - Prob. 94E Ch. 3.4 - Prob. 95E Ch. 3.4 - Prob. 96E Ch. 3.4 - Prob. 97E Ch. 3.4 - Prob. 98E Ch. 3.4 - Volume of a Silo A grain silo consists of a...Ch. 3.4 - Dimensions of a Lot A rectangular parcel of land...Ch. 3.4 - Depth of Snowfall Snow began falling at noon on...Ch. 3.4 - Volume of a Box An open box with a volume of 1500...Ch. 3.4 - Volume of a Rocket A rocket consists of a right...Ch. 3.4 - Volume of a Box A rectangular box with a volume of...Ch. 3.4 - Girth of a Box A box with a square base has length...Ch. 3.4 - DISCUSS DISCOVER: How Many Real Zeros Can a...Ch. 3.4 - Prob. 107E Ch. 3.4 - Prob. 108E Ch. 3.4 - PROVE: Upper and Lower Bounds Theorem Let P(x) be...Ch. 3.4 - Prob. 110E Ch. 3.5 - The polynomial P(x) = 5x2(x 4)3(x + 7) has degree...Ch. 3.5 - (a) If a is a zero of the polynomial P, then...Ch. 3.5 - A polynomial of degree n 1 has exactly ________...Ch. 3.5 - If the polynomial function P has real coefficients...Ch. 3.5 - True or False? If False, give a reason. 5. Let...Ch. 3.5 - True or False? If False, give a reason. 6. Let...Ch. 3.5 - Complete Factorization A polynomial P is given....Ch. 3.5 - Prob. 8E Ch. 3.5 - Prob. 9E Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Prob. 12E Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3.5 - Prob. 25E Ch. 3.5 - Prob. 26E Ch. 3.5 - Prob. 27E Ch. 3.5 - Prob. 28E Ch. 3.5 - Prob. 29E Ch. 3.5 - Prob. 30E Ch. 3.5 - Prob. 31E Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Complete Factorization Factor the polynomial...Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.5 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 51E Ch. 3.5 - Prob. 52E Ch. 3.5 - Prob. 53E Ch. 3.5 - Prob. 54E Ch. 3.5 - Prob. 55E Ch. 3.5 - Prob. 56E Ch. 3.5 - Prob. 57E Ch. 3.5 - Prob. 58E Ch. 3.5 - Prob. 59E Ch. 3.5 - Prob. 60E Ch. 3.5 - Prob. 61E Ch. 3.5 - Finding Complex Zeros Find all zeros of the...Ch. 3.5 - Finding Complex Zeros Find all zeros of the...Ch. 3.5 - Prob. 64E Ch. 3.5 - Prob. 65E Ch. 3.5 - Prob. 66E Ch. 3.5 - Prob. 67E Ch. 3.5 - Prob. 68E Ch. 3.5 - Prob. 69E Ch. 3.5 - Prob. 70E Ch. 3.5 - Prob. 71E Ch. 3.5 - Prob. 72E Ch. 3.5 - (a) Show that 2i and 1 i are both solutions of...Ch. 3.5 - (a) Find the polynomial with real coefficients of...Ch. 3.5 - DISCUSS: Polynomials of Odd Degree The Conjugate...Ch. 3.5 - Prob. 76E Ch. 3.6 - If the rational function y = r(x) has the vertical...Ch. 3.6 - If the rational function y = r(x) has the...Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - True or False? 8. The graph of a rational function...Ch. 3.6 - Prob. 9E Ch. 3.6 - Table of Values A rational function is given. (a)...Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Graphing Rational Functions Using Transformations...Ch. 3.6 - Prob. 14E Ch. 3.6 - Graphing Rational Functions Using Transformations...Ch. 3.6 - Prob. 16E Ch. 3.6 - Prob. 17E Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 19E Ch. 3.6 - Prob. 20E Ch. 3.6 - Prob. 21E Ch. 3.6 - Prob. 22E Ch. 3.6 - Prob. 23E Ch. 3.6 - Prob. 24E Ch. 3.6 - Prob. 25E Ch. 3.6 - Prob. 26E Ch. 3.6 - Prob. 27E Ch. 3.6 - Prob. 28E Ch. 3.6 - Getting Information from a Graph From the graph,...Ch. 3.6 - Prob. 30E Ch. 3.6 - Prob. 31E Ch. 3.6 - Prob. 32E Ch. 3.6 - Prob. 33E Ch. 3.6 - Prob. 34E Ch. 3.6 - Prob. 35E Ch. 3.6 - Prob. 36E Ch. 3.6 - Prob. 37E Ch. 3.6 - Prob. 38E Ch. 3.6 - Prob. 39E Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Prob. 42E Ch. 3.6 - Prob. 43E Ch. 3.6 - Prob. 44E Ch. 3.6 - Prob. 45E Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - Prob. 48E Ch. 3.6 - Prob. 49E Ch. 3.6 - Prob. 50E Ch. 3.6 - Graphing Rational Functions Find the intercepts...Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Graphing Rational Functions Find the intercepts...Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.6 - Prob. 57E Ch. 3.6 - Prob. 58E Ch. 3.6 - Prob. 59E Ch. 3.6 - Prob. 60E Ch. 3.6 - Prob. 61E Ch. 3.6 - Prob. 62E Ch. 3.6 - Prob. 63E Ch. 3.6 - Prob. 64E Ch. 3.6 - Prob. 65E Ch. 3.6 - Prob. 66E Ch. 3.6 - Prob. 67E Ch. 3.6 - Prob. 68E Ch. 3.6 - Prob. 69E Ch. 3.6 - Prob. 70E Ch. 3.6 - Prob. 71E Ch. 3.6 - Prob. 72E Ch. 3.6 - Prob. 73E Ch. 3.6 - Prob. 74E Ch. 3.6 - Prob. 75E Ch. 3.6 - Prob. 76E Ch. 3.6 - Prob. 77E Ch. 3.6 - Prob. 78E Ch. 3.6 - Prob. 79E Ch. 3.6 - End Behavior Graph the rational function f, and...Ch. 3.6 - Prob. 81E Ch. 3.6 - Prob. 82E Ch. 3.6 - End Behavior Graph the rational function, and find...Ch. 3.6 - End Behavior Graph the rational function, and find...Ch. 3.6 - Prob. 85E Ch. 3.6 - Prob. 86E Ch. 3.6 - Population Growth Suppose that the rabbit...Ch. 3.6 - Drug Concentration After a certain drug is...Ch. 3.6 - Drug Concentration A drug is administered to a...Ch. 3.6 - Flight of a Rocket Suppose a rocket is fired...Ch. 3.6 - The Doppler Effect As a train moves toward an...Ch. 3.6 - Focusing Distance For a camera with a lens of...Ch. 3.6 - Prob. 93E Ch. 3.6 - Prob. 94E Ch. 3.6 - DISCOVER: Transformations of y = 1/x2 In Example 2...Ch. 3.7 - To solve a polynomial inequality, we factor the...Ch. 3.7 - To solve a rational inequality, we factor the...Ch. 3.7 - Prob. 3E Ch. 3.7 - Prob. 4E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 5....Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 9....Ch. 3.7 - Prob. 10E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 11....Ch. 3.7 - Prob. 12E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 13....Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - Prob. 16E Ch. 3.7 - Prob. 17E Ch. 3.7 - Prob. 18E Ch. 3.7 - Rational Inequalities Solve the inequality. 19....Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E Ch. 3.7 - Prob. 22E Ch. 3.7 - Prob. 23E Ch. 3.7 - Prob. 24E Ch. 3.7 - Prob. 25E Ch. 3.7 - Prob. 26E Ch. 3.7 - Prob. 27E Ch. 3.7 - Rational Inequalities Solve the inequality. 28....Ch. 3.7 - Prob. 29E Ch. 3.7 - Prob. 30E Ch. 3.7 - Rational Inequalities Solve the inequality. 31....Ch. 3.7 - Prob. 32E Ch. 3.7 - Rational Inequalities Solve the inequality. 33....Ch. 3.7 - Prob. 34E Ch. 3.7 - Prob. 35E Ch. 3.7 - Prob. 36E Ch. 3.7 - Prob. 37E Ch. 3.7 - Prob. 38E Ch. 3.7 - Graphs of Two Functions Find all values of x for...Ch. 3.7 - Prob. 40E Ch. 3.7 - Domain of a Function Find the domain of the given...Ch. 3.7 - Prob. 42E Ch. 3.7 - Domain of a Function Find the domain of the given...Ch. 3.7 - Prob. 44E Ch. 3.7 - Prob. 45E Ch. 3.7 - Prob. 46E Ch. 3.7 - Prob. 47E Ch. 3.7 - Prob. 48E Ch. 3.7 - Prob. 49E Ch. 3.7 - Prob. 50E Ch. 3.7 - Prob. 51E Ch. 3.7 - Prob. 52E Ch. 3.7 - Prob. 53E Ch. 3.7 - Prob. 54E Ch. 3.7 - Bonfire Temperature In the vicinity of a bonfire...Ch. 3.7 - Stopping Distance For a certain model of car the...Ch. 3.7 - Managing Traffic A highway engineer develops a...Ch. 3.7 - Prob. 58E Ch. 3 - (a) What is the degree of a quadratic function f?...Ch. 3 - Prob. 2RCC Ch. 3 - Prob. 3RCC Ch. 3 - Prob. 4RCC Ch. 3 - Prob. 5RCC Ch. 3 - Prob. 6RCC Ch. 3 - Prob. 7RCC Ch. 3 - Prob. 8RCC Ch. 3 - Prob. 9RCC Ch. 3 - Prob. 10RCC Ch. 3 - Prob. 11RCC Ch. 3 - Prob. 12RCC Ch. 3 - Prob. 13RCC Ch. 3 - Prob. 14RCC Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Profit The profit P (in dollars) generated by...Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Strength of a Beam The strength S of a wooden beam...Ch. 3 - Volume A small shelter for delicate plants is to...Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Number of Possible Zeros A polynomial P is given....Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Graphing Rational Functions Graph the rational...Ch. 3 - Prob. 83RE Ch. 3 - Prob. 84RE Ch. 3 - Prob. 85RE Ch. 3 - Prob. 86RE Ch. 3 - Prob. 87RE Ch. 3 - Prob. 88RE Ch. 3 - Prob. 89RE Ch. 3 - Prob. 90RE Ch. 3 - Prob. 91RE Ch. 3 - Prob. 92RE Ch. 3 - Prob. 93RE Ch. 3 - Prob. 94RE Ch. 3 - Prob. 95RE Ch. 3 - Polynomial Inequalities Solve the inequality. 96....Ch. 3 - Prob. 97RE Ch. 3 - Prob. 98RE Ch. 3 - Prob. 99RE Ch. 3 - Prob. 100RE Ch. 3 - Prob. 101RE Ch. 3 - Prob. 102RE Ch. 3 - Prob. 103RE Ch. 3 - Prob. 104RE Ch. 3 - Prob. 105RE Ch. 3 - Prob. 106RE Ch. 3 - Express the quadratic function f(x) = x2 x 6 in...Ch. 3 - Find the maximum or minimum value of the quadratic...Ch. 3 - A cannonball fired out to sea from a shore battery...Ch. 3 - Graph the polynomial P(x) = (x + 2)3 + 27, showing...Ch. 3 - (a) Use synthetic division to find the quotient...Ch. 3 - Let P(x) = 2x3 5x2 4x + 3. (a) List all possible...Ch. 3 - Find all real and complex zeros of P(x) = x3 x2 ...Ch. 3 - Find the complete factorization of P(x) = x4 2x3...Ch. 3 - Find a fourth-degree polynomial with integer...Ch. 3 - Let P(x) = 2x4 7x3 + x2 18x + 3. (a) Use...Ch. 3 - Consider the following rational functions:...Ch. 3 - Prob. 12T Ch. 3 - Prob. 13T Ch. 3 - Prob. 14T Ch. 3 - Tire Inflation and Treadwear Car tires need to be...Ch. 3 - Too Many Corn Plants per Acre? The more corn a...Ch. 3 - How Fast Can You List Your Favorite Things? If you...Ch. 3 - Height of a Baseball A baseball is thrown upward,...Ch. 3 - Torricelli's Law Water in a tank will flow out of...

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The intercepts and asymptotes of the rational function s ( x ) = 4 x − 8 ( x − 4 ) ( x + 1 ) , sketch the graph of this function and state the domain and range. Prove the answer by graphing device.

Solution Summary: The author evaluates the intercepts and asymptotes of the rational function s(x)=4x-8, and states the domain and range.

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To evaluate: The intercepts and asymptotes of the rational function s(x)=4x−8(x−4)(x+1) , sketch the graph of this function and state the domain and range. Prove the answer by graphing device.

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Chapter 3 Solutions