Explanation Procedure used: “To graph a rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) have no common factors other than constants: 1. Find any real zeros of the denominator. Determine the domain of the function and sketch any vertical asymptotes. 2. Find the horizontal asymptote or the oblique asymptote, if there is one, and sketch it. 3. Find any zeros of the function. The zeros are found by determining the zeros of the numerator. These are the first coordinates of the x -intercepts of the graph. 4. Find f ( 0 ) . This gives the y - intercept, ( 0 , f ( 0 ) ) , of the function. 5. Find other function values to determine the general shape. Then draw the graph.” Definition used: “For a rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) are polinomials with no common factors other than constants, if a is a zero of the denominator, then the line x = a is a vertical asymptote for the graph of the function.” “When the numerator and the denominator of a rational function have the same degree, the line y = a / b is the horizontal asymptote, where a and b are the leading coefficients of the numerator and the denominator, respectively. When the degree of the numerator of a rational function is less than the degree of the denominator, the x -axis, or y = 0 , is the horizontal asymptote. When the degree of the numerator of a rational function is greater than the degree of the denominator, there is no horizontal asymptote.” Calculation: The given function is f ( x ) = 2 x 3 + x 2 − 8 x − 4 x 3 + x 2 − 9 x − 9

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ISBN: 9780134383385

Author: Penna

Publisher: VST

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Chapter 4.5, Problem 99E

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To graph: The function f(x)=2x3+x2−8x−4x3+x2−9x−9.

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Chapter 4.5, Problem 98E

Chapter 4.5, Problem 100E

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To graph: The function f ( x ) = 2 x 3 + x 2 − 8 x − 4 x 3 + x 2 − 9 x − 9 .

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To graph: The function f(x)=2x3+x2−8x−4x3+x2−9x−9.

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