Question

On a separate sheet of paper, graph the function. In the answer box, describe the function.

Xux)
-3(x+6) if x <-4
10.5(x - 8) ifx2-4

Answer 1

Answer

Explanation:

The function is a piece-wise defined function and is linear on both intervals. There is no break in the graph.

Answer 2

See attachment

Explanation:

We want to graph the piece-wise function
`f(x)=\left \{ {{-3(x+6),\:\:x<-4} \atop {0.5(x-8)\:\:,x\ge-4}} \right.`

We need to graph the linear function
`y=-3(x+6)` on the interval
`x\:<\:-4`.

Expand to get:

`y=-3x-18`

The graph has a slope of -3 and x-intercept at (-6,0).

We plot the point (-4,-6) as a hole.

Draw a straight line through the two points but it shouldn't cross the whole.

The second line is
`y=0.5(x-8)` on the interval
`x\ge -4`

Expand to get:

`y=0.5x-4`

The graph has a slope of 0.5 and a y-intercept of -4.

We draw a straight line through (-4,-6) and the y-intercept to obtain the graph of the piece-wise function as shown in the attachment.