Answer
$f(x)=\left\{\begin{array}{ll}
2x+2 & - 1 \leq x\leq 0\\
x & x\ \gt0
\end{array}\right.$
(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:
$f(x)=\left\{\begin{array}{ll}
2x+2 & - 1 \leq x\leq 0\\
x & x\ \gt0
\end{array}\right.$
