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: 33


$f(x)=\frac{2x^2}{x^2-4}$ matches the graph labeled (c)

Work Step by Step

The vertical asymptote is: $x^2-4=0$ $x^2=4$ $x=\pm2$ The x-intercept: $f(x)=\frac{2x^2}{x^2-4}=0$. $x^2=0$ $x=0$ The graph passes through the origin. The degree of the denominator is equal to the degree of the numerator. The horizontal asymptote is the ratio of the leading coefficients: $y=\frac{2}{1}=2$
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