College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.4 - Library of Functions; Piecewise-defined Function - 3.4 Assess Your Understanding: 45

Answer

$f(x)=\left\{\begin{array}{ll} -x & x\ \leq 0\\ -x+2 & 0\lt x\leq 2 \end{array}\right.$ (Other answers are also possible.)

Work Step by Step

We see that both pieces of the graph correspond to lines with slope $-\frac{1}{1}=-1$. The left line has a $y$ intercept of $0$, while the right line has a $y$ intercept of $2$. Thus the equation is: $f(x)=\left\{\begin{array}{ll} -x & x\ \leq 0\\ -x+2 & 0\lt x\leq 2 \end{array}\right.$
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