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 402: 124


The graph is shown below:

Work Step by Step

Consider the functions, $f\left( x \right)=\frac{{{x}^{2}}-4x+3}{x-2}$ and $g\left( x \right)=\frac{{{x}^{2}}-5x+6}{x-2}$. The graph of the functions $f\left( x \right)=\frac{{{x}^{2}}-4x+3}{x-2}$ and $g\left( x \right)=\frac{{{x}^{2}}-5x+6}{x-2}$ can be plotted using the TI-83 in the steps given below: Step 1: Write the function ${{Y}_{1}}=\frac{{{x}^{2}}-4x+3}{x-2}$ and ${{Y}_{2}}=\frac{{{x}^{2}}-5x+6}{x-2}$. Step 2: After that, set the window from $\left( -5,5,1 \right)$ on the $x$ -axis and $\left( -5,5,1 \right)$ on the $y$ -axis. Step 3: Then, press TRACE. As can be observed from the above graph that the function $f$ is symmetric about the line $x=2$. And, it has a vertical asymptote at $x=2$ , a slant asymptote at $x-2=0$ , and no horizontal asymptote. Also, the graph $g$ is a straight line and passes through the points $\left( 0,-3 \right)$ and $\left( 0,3 \right)$. And, the graph $g$ has no vertical and horizontal asymptote.
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