Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 208: 78

Answer

Graphing as instructed, we see that the graph of (b) is obtained by reflecting the graph of (a) about the x-axis.. Vertically stretching by factor 3 gives graph (c), and shifting 5 units to the right produces graph (d).

Work Step by Step

Taking (a) $y=f(x)=|x|,$ we find that (b) $y=-f(x),$ (c) $y=3\cdot[-f(x)]=-3f(x)$ (d) $y=-3f(x-5)$ So, the graph of (b) is obtained by reflecting the graph of (a) about the x-axis.. Vertically stretching by factor 3 gives graph (c), and shifting 5 units to the right produces graph (d).
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