Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 399: 74

Answer

Graph the function as:
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Work Step by Step

Step 1: Substitute $x=-x.$ $\begin{align} & f\left( x \right)=\frac{x-3}{{{x}^{2}}-9} \\ & f\left( -x \right)=\frac{\left( -x \right)-3}{{{\left( -x \right)}^{2}}-9} \\ & =\frac{-x-3}{{{x}^{2}}-9} \\ & \ne -f\left( x \right) \end{align}$ Therefore, the function $f\left( -x \right)$ is not equal to $-f\left( x \right)$ and the function $f\left( x \right)$. The graph of the function is not symmetric about $y\text{-}$ axis and origin. Step 2: To calculate the x intercepts equate $f\left( x \right)=0$. There are no values of x for which the equation holds true, hence there are no x intercepts. Step 3: To calculate the y intercepts evaluate $f\left( 0 \right)$. $f\left( 0 \right)=\frac{1}{3}$ Step 4: Since the degree of the numerator is less than the denominator, there is no horizontal asymptote. Step 5: For the vertical asymptote, equate the denominator to 0. $x=-3$
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