Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Section 1.5 Graphing Techniques: Transformations - 1.5 Assess Your Understanding - Page 98: 37

Answer

(a) $(-3,3)$; (b) $(4,10)$; (c) decreasing interval $(-1,5)$; (d) decreasing interval $(-5,1)$.

Work Step by Step

Given an increasing interval $(-1,5)$ of $y=f(x)$, we have: (a) For $y=f(x+2)$, shift the x-coordinates 2 units to the left, thus new increasing interval $(-3,3)$; (b) For $y=f(x-5)$, shift the x-coordinates 5 units to the right, thus new increasing interval $(4,10)$; (c) For $y=-f(x)$, reflect across the x-axis, thus we have a new decreasing interval $(-1,5)$; (d) For $y=f(-x)$, reflect across the y-axis, thus we have a new decreasing interval $(-5,1)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.