Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.1 - Exponential Functions and Their Graphs - 5.1 Exercises - Page 368: 31

Answer

It is necessary to reflect $f(x)$ about the y-axis and then, move the new graph 3 units to the right.

Work Step by Step

Observe: $f(0)=10^0=1$ which gives the point: $(0,1)$ $g(3)=10^{-3+3}=10^0=1$ which gives the point: $(3,1)$ $f(1)=10^1=10$ which gives the point: $(1,10)$ $g(2)=10^{-2+3}=10^1=10$ which gives the point: $(2,10)$ $f(2)=10^2=100$ which gives the point: $(2,100)$ $g(1)=10^{-2+3}=10^2=100$ which gives the point: $(1,100)$ That is, $f(x)$ and $g(x)$ increase in opposite directions. In order to obtain $g(x)$ it is necessary to reflect $f(x)$ about the y-axis and then, move the new graph 3 units to the right.
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