Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 2 - Functions, Equations, and Graphs - 2-7 Absolute Value Functions and Graphs - Practice and Problem-Solving Exercises - Page 111: 21

Answer

The graph of the given function involves a vertical stretch by a factor of $\frac{3}{2}$ of the parent function $y=|x|$. Refer to the blue graph below.
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Work Step by Step

RECALL: The graph of the function $y=a|x|$ involves a vertical stretch by a factor of $|a|$ of the parent function $y=|x|$. The given function has $a=\frac{3}{2}$ therefore the graph of $y=\frac{3}{2}|x|$ involves a vertical stretch by a factor of $\frac{3}{2}$ of the parent function $y=|x|$. To graph the given function, vertucally stretch the graph of $y=|x|$ by a factor of $\frac{3}{2}$. This can be done by multiplying each $y$-value of $y=|x|$ by $\frac{3}{2}$ (while retaining the value of $x$). Refer to the blue graph above.
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