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 - Page 409: 44


See the picture below.

Work Step by Step

The parent function is $f(x)=(\frac{1}{3})^x$ (with red) the given function is $g(x)=(\frac{1}{3})^{x-4}$ (with blue). The parent function can be graphed by calculating a few coordinates and connecting them with a smooth curve: $f(-2)=(\frac{1}{3})^{-2}=9$ $f(-1)=(\frac{1}{3})^{-1}=3$ $f(0)=(\frac{1}{3})^0=1$ $f(1)=(\frac{1}{3})^1=\frac{1}{3}$ $f(2)=(\frac{1}{3})^2=\frac{1}{9}$ For every corresponding x-value the following equation is true: $f(x-4)=g(x)$ This means that the graph is translated 4 units right ($g(x)$ involves a horizontal shift of 4 to the right). Because when f(x)=g(x), the g(x) function acts like the f(x). For example if $f(0)=1$ in the original $f(x)$, this will be equal to $g(4)=f(4-4)=f(0)=1$. $Here, f(0)=g(4)$ also, $f(1)=g(5)$ We can see that here, each point in the parent function was moved to the right by 4 units.
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