Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 4 - 4.1 - Rational Functions and Asymptotes - 4.1 Exercises - Page 315: 35


$f(x)=\frac{x^3}{4(x+2)^2}$ matches with the graph labeled (d).

Work Step by Step

The vertical asymptote is: $4(x+2)^2=0$ $(x+2)^2=0$ $x+2=0$ $x=-2$ The x-intercept: $f(x)=\frac{x^3}{4(x+2)^2}=0$. $x^3=0$ $x=0$ The graph passes through the origin. The degree of the numerator is greater than the degree of the denominator. The graph has no horizontal asymptotes.
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