The piecewise function is given to be:
[tex]f(x)=\begin{cases}{3\text{ if }x>0} \\ {1\text{ if }x=0} \\ {x-1\text{ if }x<0}\end{cases}[/tex]
For the first part, we have the following graph:
[tex]\begin{gathered} f(x)=3 \\ if \\ x>0 \end{gathered}[/tex]
For the second part, we have the following graph:
[tex]\begin{gathered} f(x)=1 \\ if \\ x=0 \end{gathered}[/tex]
For the third part, we have the graph:
[tex]\begin{gathered} f(x)=x-1 \\ if \\ x<0 \end{gathered}[/tex]
Therefore, OPTION C is correct.
