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: 29

Answer

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

RECALL: The graph of the function $f(x) = -a^x$ involves a reflection about the x=axis of the parent function $y = a^x$. The given function $f(x) = -3^x$ has its parent function $y = 3^x$. The graph of the given function is a reflection about the x-axis of the parent function. Thus, to graph the given function, perform the following steps: (1) Graph the parent function $y = 3^x$ 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 reflecting the points of the parent function about the x-axis. This can be achieved by plotting the negative (or opposite sign) of each y-value of the parent function (e.g., if (0, 1) is in the parent function, (0, -1) is in f(x)). 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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