The first piece passes through the points (-6,-9) and (-1,-4) so the equaton of first piece is:
[tex]\begin{gathered} \frac{y+9}{x+6}=\frac{-4+9}{-1+6} \\ y+9=x+6 \\ y=f(x)=x-3 \end{gathered}[/tex]
The second piece passes through the points (2,-5) and (3,-6) so it follows:
[tex]\begin{gathered} \frac{y-(-5)}{x-2}=\frac{-6-(-5)}{3-2} \\ y+5=-x+2 \\ y=f(x)=-x-3 \end{gathered}[/tex]
Hence the piecewise function is given by:
[tex]f(x)=\begin{cases}x-3,-6\leq x<1 \\ -x-3,1
The above function is the required piecewise function.
