Question

Express the function graphed on the axes below as a piecewise function.108642-10-8-6-426810-8

Answer 1

The first piece passes through the points (-6,-9) and (-1,-4) so the equaton of first piece is:

`\begin{gathered} (y+9)/(x+6)=(-4+9)/(-1+6) \\ y+9=x+6 \\ y=f(x)=x-3 \end{gathered}`

The second piece passes through the points (2,-5) and (3,-6) so it follows:

`\begin{gathered} (y-(-5))/(x-2)=(-6-(-5))/(3-2) \\ y+5=-x+2 \\ y=f(x)=-x-3 \end{gathered}`

Hence the piecewise function is given by:

[tex]f(x)=\begin{cases}x-3,-6\leq x<1 \\ -x-3,1The above function is the required piecewise function.