Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 42: 1

Answer

a) $y = f(x) + 3$ b) $y = f(x)-3$ c) $y = f(x-3)$ d) $y = f(x+3)$ e) $y = -f(x)$ f) $y = f(-x)$ g) $y = 3f(x)$ h) $y = f(\frac{1}{3}x)$

Work Step by Step

a) You add 3 to the end of the function to shift it 3 units upwards $y = f(x) + 3$ b) You subtract 3 from the end of the function to shift it 3 units downwards. $y = f(x)-3$ c) You subtract 3 from the x within the function to shift the function 3 units to the right. $y = f(x-3)$ d) You add 3 to the x within the function to shift the function 3 units to the left. $y = f(x+3)$ e) You multiply the entire function to reflect it over the x-axis. $y = -f(x)$ f) You multiply the x within the function to reflect it over the y-axis. $y = f(-x)$ g) You multiply the entire function by 3 to vertically stretch it by 3. $y = 3f(x)$ h) You multiply the x within the function by $\frac{1}{3}$ to horizontally stretch it by 3. $y = f(\frac{1}{3}x)$
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