Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Review - Concept Check: 11

Answer

(a) $y=f(x)+2$ (b) $y=f(x)-2$ (c) $y=f(x-2)$ (d) $y=f(x+2)$ (e) $y=-f(x)$

Work Step by Step

(a) $y=f(x)+2$ Because by adding two we increase every value of the function by $2$ and the points move upwards by $2$ units. (b) $y=f(x)-2$ Because by subtracting two we decrease every value of the function by $2$ and the points move downwards by $2$ units. (c) $y=f(x-2)$ Because everything that "happened" to the function at $x$ now will happen two units "latter" i.e. the graph will shift to the right. (d) $y=f(x+2)$ Because everything that "happened" to the function at $x$ now will happen "earlier" i.e. the graph will shift to the left. (e) $y=-f(x)$ Because every value will change its sign so the points of the graph will reflect with respect to $y$ axis.
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