Answer:
See attachment
Step-by-step explanation:
We want to graph the piece-wise function [tex]f(x)=\left \{ {{-3(x+6),\:\:x<-4} \atop {0.5(x-8)\:\:,x\ge-4}} \right.[/tex]
We need to graph the linear function [tex]y=-3(x+6)[/tex] on the interval [tex]x\:<\:-4[/tex].
Expand to get:
[tex]y=-3x-18[/tex]
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 [tex]y=0.5(x-8)[/tex] on the interval [tex]x\ge -4[/tex]
Expand to get:
[tex]y=0.5x-4[/tex]
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.
