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 400: 97


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Work Step by Step

Consider the function $g\left( x \right)=\frac{3x+7}{x+2}$ and convert into the form: $\text{Quotient}+\frac{\text{Remainder}}{\text{Divisor}}$. $\begin{align} & g\left( x \right)=\frac{3x-7}{x-2} \\ & g\left( x \right)=3+\frac{\left( -1 \right)}{x-2} \end{align}$ where quotient is $3$ , remainder is $-1,$ and divisor is $x-2$. The rational root is $\begin{align} & x-2=0 \\ & x=2 \end{align}$ The graph of the function $f\left( x \right)=-\frac{1}{x}$ is the mirror image of the function $f$ about the x-axis. When x is changed to x-a, this implies that the graph of the function is shifted by a units to the right. The graph is shifted to the right by 2 units: $f\left( x \right)=\frac{-1}{x-2}$. Now, shift the graph 3 units upward $\frac{-1}{x-2}$, to give the final graph. The graph has a vertical asymptote along $x=2$. The graph has a horizontal asymptote along $y=3$
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