Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 2 - Functions - 2.4 Preview of Transformations: Shifts - Exercises and Problems for Section 2.4 - Exercises and Problems - Page 97: 23


A shift of $q(z)$ $b$ units to the left and $a$ units downward graphically.

Work Step by Step

The transformation $f(x)$ to $f(x-a)$ for all positive values of $a$ results in a rightward shift of $a$ units graphically. However, this is a shift of $q(x-(-b))=q(x+b)$, or $b$ units leftward. The transformation $g(x)$ to $g(x)-a$ results in a downward shift of $a$ units for all positive values, so the graph will be shifted down $a$ units.
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