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: 34


See the picture below.

Work Step by Step

The parent function is $f(x)=2^x$ (with red) the given function is $g(x)=-2^{x-3}$ (with blue). For every corresponding x-value the following equation is true: $-f(x-3)=g(x)$ This means that the graph is translated 3 units right. Every x-value will be increased by 3. (Because the original f(x) will be equal to f(x-3). For example if x=0 in the original f(0), this will be translated as f(3-3), where x=3. We can see that here, x has increased by 3.) After that it is also reflected across the x-axis. (Because of the -1 coefficient before f(x-3))
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