Question

Express the function graphed on the axes below as a piecewise function.10802-108-6-422246810-10

Answer 1

From the graph it is clear that the function is a horizontal line from -6 to -3 and an oblique line from -3 to 3 so the equation from -6 to -3 is:

$f(x)=5$

The equation of line using two point form from -3 to 3 is found by knowing the points.The line passes through (-2,6) and (0,4) so it follows:

$\begin{gathered} \frac{y-6}{x+2}=\frac{4-6}{0+2} \\ y-6=-(x+2) \\ y=-x-2+6=-x+4 \\ y=f(x)=-x+4 \end{gathered}$

Hence the piecewise function is given by:

[tex]f(x)=\begin{cases}5,-6\leq x<-3 \\ -x+4,-3Hence the function shown above is the required piecewise function.