Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 176: 41

Answer

See the full explanation below.

Work Step by Step

We plot the graphs for $f\left( x \right)=-2x$ and $g\left( x \right)=-2x-1$ with the help of the points individually for $f\left( x \right)$ and $g\left( x \right)$. We find the coordinates of $f\left( x \right)$ for $x=-2$ to $x=2$ as follows: $\begin{align} & x=-2 \\ & f\left( x \right)=-2x \\ & =-2\left( -2 \right) \\ & =4 \end{align}$ $\begin{align} & x=-1 \\ & f\left( x \right)=-2x \\ & =-2\left( -1 \right) \\ & =2 \end{align}$ $\begin{align} & x=0 \\ & f\left( x \right)=-2x \\ & =-2\left( 0 \right) \\ & =0 \end{align}$ $\begin{align} & x=1 \\ & f\left( x \right)=-2x \\ & =-2\left( 1 \right) \\ & =-2 \end{align}$ $\begin{align} & x=2 \\ & f\left( x \right)=-2x \\ & =-2\left( 2 \right) \\ & =-4 \end{align}$ We find the coordinates of $g\left( x \right)=-2x-1$ for $x=-2$ to $x=2$ as follows: $\begin{align} & x=-2 \\ & g\left( x \right)=-2x-1 \\ & =-2\left( -2 \right)-1 \\ & =3 \end{align}$ $\begin{align} & x=-1 \\ & g\left( x \right)=-2x-1 \\ & =-2\left( -1 \right)-1 \\ & =1 \end{align}$ $\begin{align} & x=0 \\ & g\left( x \right)=-2x-1 \\ & =-2\left( 0 \right)-1 \\ & =-1 \end{align}$ $\begin{align} & x=1 \\ & g\left( x \right)=-2x-1 \\ & =-2\left( 1 \right)-1 \\ & =-3 \end{align}$ $\begin{align} & x=2 \\ & g\left( x \right)=-2x-1 \\ & =-2\left( 2 \right)-1 \\ & =-5 \end{align}$
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