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 - Page 245: 46


$f(x)=\left\{\begin{array}{ll} 2x+2 & - 1 \leq x\leq 0\\ x & x\ \gt0 \end{array}\right.$ (Other answers are also possible.)

Work Step by Step

We see that the left side of the graph corresponds to a line with a slope of $\frac{2}{1}=2$ and a $y$-intercept of $2$, i.e. $y=2x+2$. The line on the right side has a slope of $\frac{2}{2}=1$ and a $y$-intercept of $0$, i.e. $y=x$. Thus the equation is: $f(x)=\left\{\begin{array}{ll} 2x+2 & - 1 \leq x\leq 0\\ x & x\ \gt0 \end{array}\right.$
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