College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises: 41


See the picture below.

Work Step by Step

The parent function is $g(x)=(\frac{1}{3})^x$ (with red) the given function is $f(x)=(\frac{1}{3})^x-2$ (with blue). The parent function can be graphed by calculating a few coordinates and connecting them with a smooth curve: $g(-2)=\frac{1}{3}^{-2}=9$ $g(-1)=\frac{1}{3}^{-1}=3$ $g(0)=\frac{1}{3}^0=1$ $g(1)=\frac{1}{3}^1=\frac{1}{3}$ $g(2)=\frac{1}{3}^2=\frac{1}{9}$ For every corresponding x-value the following equation is true: $g(x)-2=f(x)$ This means that the graph is translated 2 units down. Every $g(x)$ value will be decreased by 2. (Because the original $f(x)$ will be equal to $(x)-2$ with the same x-value. For example if $f(0)=1$ in the original $f(x)$, this will be translated as $g(0)-2=1-2=-1$. We can see that here, the $g(x)$ is greater than $f(x)$ for every corresponding x-value by 2.)
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