Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises: 43

Answer

$$f(x)=|x-2|+3,\quad g(x)=-|x+2|-1.$$
1517790383

Work Step by Step

1) The purple function. We see that it has a cusp when $x=2$ and $y=3$. This means that the function $y=|x|$ has to be shifted upwards by $3$ and rightwards by $2$. There is no rescaling since the function in the linear pieces increases or decreases by $1$ unit when $x$ changes by $1$ so the equation is $$y=|x-2|+3.$$ 2) The blue function. This function has a cusp when $x=-2$ and $y=-1$ and it point upwards which means that it is inverted with respect to $y=|x|$. There are several ways to obtain this function, one of them is: invert it with respect to $x$ axis and then shift it leftwards by $2$ and downwards by $1$: a) Inversion $|x|\to-|x|$; b) Leftwards shift $-|x|\to-|x+2|$ c) Downwards shift $-|x+2|\to-|x+2|-1$ The function is then $$y=-|x+2|-1.$$ Their graphs are in the figure below
Small 1517790383
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.