Question

Can someone help?

Express the function graphed on the axes below as a piecewise function.​

Answer 1

`\displaystyle f(x) = \begin{cases} x+3 & \text{if $-5<x<0$} \\ -(1)/(2)x-1 & \text{if $0<x\leq6$} \end{cases}`

Explanation:

Observing the graph, we see two functions:

`f(x)=x+3` but x<0 and x>-5

`f(x)=-(1)/(2)x-1` 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:

`\displaystyle f(x) = \begin{cases} x+3 & \text{if $-5<x<0$} \\ -(1)/(2)x-1 & \text{if $0<x\leq6$} \end{cases}`