Question

Complete the equation for the piece wise function graphed below.

Answer 1

The equation then becomes:

`y=-0.5x+b`

Using the point (-6,0)

`\begin{gathered} 0=-0.5(6)+b \\ b=3 \end{gathered}`

Therefore: f(x)=-0.5x+3, -6≤x≤-2

Next, f(x)=-3 for -2

Finally, for 1The endpoints are (1,-4) and (6,1)

`\text{Slope,m}=(-4-1)/(1-6)=(-5)/(-5)=1`

Using the point (1,-4)

`\begin{gathered} y=mx+b \\ -4=1(1)+b \\ b=-4-1=-5 \end{gathered}`

Therefore, f(x)=x-5, for 1

The completed function will now be:

[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,-6\le x\le-2 \\ -3,-2