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: 28


Refer to the image below for the graph. The graph of $h(x)$ is red, the graph of the parent function is blue.

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 $h(x) = 4+(\frac{1}{2})^x$ has its parent function $f(x) = (\frac{1}{2})^x$. The given function has $k=4$ so it involves a 4-unit upward shift of the graph of its parent function. Thus, to graph the given function, perform the following steps: (1) Graph the parent function $f(x) = (\frac{1}{2})^x$ by 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 $h(x)$by moving the graph of the parent function 4 units upward. The graph of $h(x)$ 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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