Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Chapter 2 Test Prep - Review Exercises: 69

Answer

Refer to the blue graph below.
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Work Step by Step

The parent function of $f(x)=|x|-3$ is the absolute value function $y=|x|$. Graph the parent function $y=|x|$. (refer to the graph below). RECALL: The graph of the function $y=f(x)+k$ involves a vertical shift of $|k|$ units (upward when $k\gt0$, downward when $k\lt0$). The given function can be written as $f(x) = |x|=(-3)$. This equation is of the form $y=f(x)+(-3)$. Thus, with $k=-3$, the graph of the given function involves a3-unit downward shift of the parent function $y=|x|$. Graph the given function by applying a 3-unit downward shift of the graph of $y = |x|$. (Refer to the blue graph in the answer part above).
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