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: 31


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

Work Step by Step

RECALL: The graph of the function $f(x) = a^{x-h}$ involves a horizontal shift of $|h|$ units (to the right when $h$ is positive, to the left when $h$ is negative) of the parent function $y = a^x$. The given function $f(x) = 10^{x+3}$ has its parent function $y = 10^x$. The function has $h=-3$ so its graph involves a 3-unit horizontal shift to the left of the parent function. Thus, to graph the given function, perform the following steps: (1) Graph the parent function $y = 10^x$ 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 $f(x)$by shifting the points of the parent function 3 units to the left. The graph of $f(x)$ is orange, 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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