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: 49


The graph has a horizontal asymptote at $y=-2$. The graph intersects the x-axis at $\left( \frac{-1}{2},0 \right)$ and y-axis at $\left( 0,-1 \right)$

Work Step by Step

First, plot the graph for $f\left( x \right)\ =\ \frac{1}{x}$. Now, $f\left( x\ +\ a \right)$ implies that the graph is shifted leftwards by $a$ units. Plot $y\ =\ \frac{1}{x\ +\ 1}$ by shifting the graph of $f\left( x \right)\ =\ \frac{1}{x}$ $1$ unit to the left. Further, $f\left( x \right)\ -\ a$ implies a downwards shift in the graph by $a$ units. Plot $g\left( x \right)\ =\ \frac{1}{x\ +\ 1}\ -\ 2$ by shifting $y\ =\ \frac{1}{x\ +\ 1}$ down by $2$ units.
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