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 96: 12

Answer

$n(r)=m(r)+2$ $p(r)=m(r-1)$ $k(r)=m(r+1.5)$ $w(r)=m(r-0.5)-2.5$

Work Step by Step

(a) This graph is the graph of $m(r)$ shifted upwards by two units. The formula for $n(r)$ is $$ n(r)=m(r)+2 . $$ (b) This graph is the graph of $m(r)$ shifted to the right by one unit. The formula for $p(r)$ is $$ p(r)=m(r-1) $$ (c) This graph is the graph of $m(r)$ shifted to the left by 1.5 units. The formula for $k(r)$ is $$ k(r)=m(r+1.5) . $$ (d) This graph is the graph of $m(r)$ shifted to the right by 0.5 units and downwards by 2.5 units. The formula for $w(r)$ is $$ w(r)=m(r-0.5)-2.5 . $$
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