Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 102: 4

Answer

True

Work Step by Step

If we reflect a point $(x,y)$ about the x-axis, it becomes $(x,-y)$. If $y=-f(x)$, then $-y=f(x)$, then, for the same value of $x$, the value of $y$ changes to its opposite. This means that each point pf the original function is being reflected about the $x$-axis. Hence, the given statement is true.
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