Precalculus (6th Edition) Blitzer

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

Chapter 7 - Cumulative Review Exercises - Page 880: 24

Answer

The graph is shown below:
1570280197

Work Step by Step

We have to find any two solutions of the linear equation, plot the graph of the linear equation $ y={{3}^{x-2}}$ To find the value of the y-intercept, substitute $ x=0$ as given below: $\begin{align} & y={{3}^{x-2}} \\ & y={{3}^{0-2}} \\ & y={{3}^{-2}} \\ & x=\frac{1}{{{3}^{2}}} \end{align}$ $ x=\frac{1}{9}$ To find the value of the y-intercept, substitute $ x=1$ as given below: $\begin{align} & y={{3}^{x-2}} \\ & y={{3}^{1-2}} \\ & y={{3}^{-1}} \\ & y=\frac{1}{3} \end{align}$ To find the value of the y-intercept, substitute $ x=2$ as given below: $\begin{align} & y={{3}^{x-2}} \\ & y={{3}^{2-2}} \\ & y={{3}^{0}} \\ & y=1 \end{align}$ To find the value of the y-intercept, substitute $ x=-1$ as given below: $\begin{align} & y={{3}^{x-2}} \\ & y={{3}^{-1-2}} \\ & y={{3}^{-3}} \\ & y=\frac{1}{{{3}^{3}}} \end{align}$ $ y=\frac{1}{27}$ To find the value of the y-intercept, substitute $ x=-2$ as given below: $\begin{align} & y={{3}^{x-2}} \\ & y={{3}^{-2-2}} \\ & y={{3}^{-4}} \\ & y=\frac{1}{{{3}^{4}}} \end{align}$ $ y=\frac{1}{81}$ To find the value of the y-intercept, substitute $ x=3$ as given below: $\begin{align} & y={{3}^{x-2}} \\ & y={{3}^{3-2}} \\ & y={{3}^{1}} \\ & y=3 \end{align}$ Therefore, plot the intercepts $\left( 0,\frac{1}{9} \right),\left( 1,\frac{1}{3} \right)\text{,}\left( 2,1 \right)\text{,}\left( 3,3 \right)\text{,}\left( -1,\frac{1}{27} \right)\text{, and }\left( -2,\frac{1}{81} \right)$ and join them with a free hand in order to get the graph of the equation $ y={{3}^{x-2}}$
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