Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Review - Exercises: 9

Answer

(a) Shifting the graph upwards by $8$ (b) Shifting the graph leftwards by $8$ (c) Stretching the graph by the factor of $2$ vertically and then shifting it upwards by $1$ (d) Shifting the graph to the right by $2$ and then downwards by 2 (e) Reflecting the graph with respect to $x$ axis (f) Reflecting the graph with respect to the line $y=x$

Work Step by Step

(a) Shifting the graph upwards by $8$ This is because we add $8$ to $f$ (b) Shifting the graph leftwards by $8$ This is because we evaluate $f$ at $x+8$ which defines the leftward translation by $8$ (c) Stretching the graph by the factor of $2$ vertically and then shifting it upwards by $1$. This is because we first multiply $f$ by $2$ which stretches it vertically by the factor of $2$ and then we add $1$ which defines the upward translation by $1$ (d) Shifting the graph to the right by $2$ and then downwards by 2 This is because we evaluate $f$ at $x-2$ which defines the rightward translation by $2$ and then we subtract $2$ from it which defines the downward translation by $2$. (e) Reflecting the graph with respect to $x$ axis. This is because the sign of every value of $f$ will change so every point of that graph will "pass" to the other side of $x$ axis. (f) Reflecting the graph with respect to the line $y=x$. This is because every point of the graph $(x,y)$ will have its' $x$ and $y$ exchanged i.e. it will pass to $(y,x)$ which will result in the reflection about the line $y=x$.
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