College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.1 - Exponential Functions - 4.1 Exercises - Page 373: 27

Answer

Refer to the attached image below for the graph. The graph of $g(x)$ is red, the graph of the parent function is blue.
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Work Step by Step

RECALL: The graph of the function $g(x) = a^x + k$ involves a vertical shift of $|k|$ units of the parent function $f(x) = a^x$. The shift is upward when $k$ is positive and downward then $k$ is negative. The given function $g(x) = 2^x-3$ has its parent function $f(x) = 26x$. The given function has $k=-3$ so it involves a 3-unit downward shift of the graph of its parent function. Thus, to graph the given function, perform the following steps: (1) Graph the parent function $f(x) = 2^x$ creating a table of values then connecting the points using a smooth curve. (refer to the attached table below, the graph is attached in the answer part above) (2) Draw the graph of the given function by moving the graph of the parent function 1 unit downward. The graph of $g(x)$ is red, the graph of the parent function is blue. (refer to the attached image in the answer part above for the graph)
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