Answer
$$f(x)=\left\{\begin{array}{ll}
2x+2 &-1 \leq x\leq0 \\
x & x \gt 0
\end{array}\right.$$ (Other answers are also possible.)
Work Step by Step
As depicted in the graph, the left-hand side of the graph represents a line with a slope of $2$ and $y$-intercept of $2$. This corresponds to the line of $y=2x+2$.
We can also conclude from the right side of the graph that it represents a line with a slope of $1$ and $y$-intercept of $0$. This corresponds to the line of $y=x$.
Therefore, the definition for this function can be expressed as:
$$f(x)=\left\{\begin{array}{ll}
2x+2 &-1 \leq x\leq0 \\
x & x \gt 0
\end{array}\right.$$
