Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises: 2

Answer

(a) Shift the graph of $f(x)$ vertically upwards by $8$ (b) Shift the graph of $f(x)$ to the left by $8$ (c) Stretch the graph of $f(x)$ vertically by the factor of $8$ (d) Shrink the graph horizontally by the factor of $8$ (e) Reflect the graph with respect to the $x$ axis and then shift it downwards by $1$ (f) Stretch the graph both vertically and horizontally by the factor of $8$

Work Step by Step

(a) Shift the graph of $f(x)$ vertically upwards by $8$. This is because the upward translation is applied. (b) Shift the graph of $f(x)$ to the left by $8$ This is because the leftward translation is applied. (c) Stretch the graph of $f(x)$ vertically by the factor of $9$ This is because the vertical stretching transformation by factor of $8$ is applied. (d) Shrink the graph horizontally by the factor of $8$ This is because the horizontal stretching by factor of $8$ is applied. (e) Reflect the graph with respect to the $x$ axis and then shift it downwards by $1$ This is because first the reflection with respect to $x$ axis is applied and then the verical downwards translation by $1$ (f) Stretch the graph both vertically and horizontally by the factor of $8$. This is because both the vertical stretching by the factor of $8$ and horizontal stretchig by the factor of $8$ are applied.
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