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: 1

Answer

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

Work Step by Step

(a) We plot $f(x)+3$ This is because every value on the vertical axis will increase by $3$. (b) We plot $f(x)-3$ This is because every value on the vertical axis will decrease by $3$ (c) We plot $f(x-3)$ This is because everything that "happens" to $f(x)$ will happen to $f(x-3)$ three units of $x$ to the right. (d) We plot $f(x+3)$ This is because everything that "happens" to $f(x)$ will happen to $f(x+3)$ three units of $x$ to the left. (e) We plot $-f(x)$ This is because the values of the function that are on the $y$ axis change the sign. (f) We plot $f(-x)$ This is because everything that happened to the function on the one side of $y$ axis (let's say when $x$ is positive) now will happen on the other side because we take $-x$ as the argument. (g) We plot $3f(x)$ Every value of the function will be $3$ times bigger so it will appear stretched vertically. (h) We plot $\frac{1}{3}f(x)$ Every value of the function will be $3$ times smaller so it will appear shrunk vertically.
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