Answer:
[tex]\displaystyle f(x) = \begin{cases} x+3 & \text{if $-5<x<0$} \\ -\frac{1}{2}x-1 & \text{if $0<x\leq6$} \end{cases}[/tex]
Step-by-step explanation:
Observing the graph, we see two functions:
[tex]f(x)=x+3[/tex] but x<0 and x>-5
[tex]f(x)=-\frac{1}{2}x-1[/tex] but x>0 and x≤6
Because the domain is restricted for both functions and there's a jump discontinuity at x=0, this is a piecewise function. This is how it would be notated:
[tex]\displaystyle f(x) = \begin{cases} x+3 & \text{if $-5<x<0$} \\ -\frac{1}{2}x-1 & \text{if $0<x\leq6$} \end{cases}[/tex]
