Question

Complete the equation for the piece wise function graphed below.

Answer 1

Answer:

$f(x)=\mleft\{\begin{aligned}-0.5x+3,if-6\le x\le-2 \\ -3,if-2Explanation:

For the value of x such that: -6≤x≤-2

We have the endpoints (-6,0) and (-2, -2).

We determine the equation in the slope-intercept form, y=mx+b.

[tex]\begin{gathered} \text{Slope,m}=\frac{0-(-2)}{-6-(-2)} \\ =\frac{2}{-6+2} \\ =\frac{2}{-4} \\ m=-0.5 \end{gathered}$

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)

$\text{Slope,m}=\frac{-4-1}{1-6}=\frac{-5}{-5}=1$

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