# Chapter 3 - Section 3.4 - Library of Functions; Piecewise-defined Function - 3.4 Assess Your Understanding - Page 245: 44

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

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