Explanation Given: Asymptotes of the function are the lines x = ± 3 and the x axis and it passes through the points ( 0 , 0 ) and ( 4 , 8 7 ) . Formula used: For a rational function P ( x ) Q ( x ) , where degree of P ( x ) is less than degree of Q ( x ) . Vertical asymptotes are given by the zeroes of the equation Q ( x ) = 0 and the horizontal asymptotes are given by y = lim x → ∞ P ( x ) Q ( x ) . If a function y = f ( x ) passes through a point ( x 1 , y 1 ) , it must satisfy y 1 = f ( x 1 ) . Calculation: Let the function be P ( x ) Q ( x ) . 2 vertical asymptotes imply to two roots of the equation. So Q ( x ) = 0 is a quadratic equation, whose roots are x = ± 3 . Hence Q ( x ) is: ( x − 3 ) ( x + 3 ) = x 2 − 3 2 = x 2 − 9 . As the x axis is the only horizontal asymptote, degree of P ( x ) is less than degree of Q ( x ) . Degree of P ( x ) would be 1 as degree of Q ( x ) is 2. Therefore, P ( x ) = a x + b . The rational function P ( x ) Q ( x ) becomes a x + b x 2 − 9 . The point passes through ( 0 , 0 ) and ( 4 , 8 7 ) , it must satisfy y 1 = f ( x 1 ) . y = P ( x ) Q ( x ) y 1 = P ( x 1 ) Q ( x 1 ) y 1 = a x 1 + b x 1 2 − 9 Substitute y 1 = 0 and x 1 = 0 for the point ( 0 , 0 )

College Algebra Plus New Mymathlab With Pearson Etext Access Card

6th Edition

ISBN: 9780321919748

Author: Mark Dugopolski

Publisher: PEARSON

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Chapter 3.5, Problem 135E

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To calculate: The equation of a rational function whose asymptotes are the lines x=±3 and the x axis and it passes through the point’s (0,0) and (4,87). Also sketch its graph.

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Chapter 3.5, Problem 134E

Chapter 3.5, Problem 136E

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Chapter 3 Solutions

College Algebra Plus New Mymathlab With Pearson Etext Access Card

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The equation of a rational function whose asymptotes are the lines x = ± 3 and the x axis and it passes through the point’s ( 0 , 0 ) and ( 4 , 8 7 ) . Also sketch its graph.

Solution Summary: The author explains the equation of a rational function whose asymptotes are the lines x=pm 3 and the X axis and it passes through the points.

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To calculate: The equation of a rational function whose asymptotes are the lines x=±3 and the x axis and it passes through the point’s (0,0) and (4,87). Also sketch its graph.

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Chapter 3 Solutions