Answer:
option B
Step-by-step explanation:
We have three different function for h(x)
[tex]h(x)= \frac{1}{4}x-4, x<=0[/tex]
WE have x<=0, so the graph starts at x=0 and goes down
Plug in 0 for x
[tex]h(0)= \frac{1}{4}(0)-4[/tex]
So h(0)= -4
When x=0, y= -4
The graph starts at (0,-4) and goes down
[tex]h(x)= \frac{1}{3}x-3, 0<x<=3[/tex]
x lies between 0 and 3, so the graph starts at x=0 and ends at x=3
Plug in 0 for x
[tex]h(0)= \frac{1}{3}(0)-3[/tex]
So h(0)= -3
When x=0, y= -4
Plug in 3 for x
[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]
When x=3, y= -2
The graph starts at (0,-4) and ends at (3, -2)
[tex]h(x)= \frac{1}{2}x-2, x>=4[/tex]
WE have x>=4, so the graph starts at x=4 and goes to the right
Plug in 4 for x
[tex]h(4)= \frac{1}{2}(4)-2[/tex]
So h(4)= 0
When x=4, y= 0
The graph starts at (4,0) and goes to the right.
SEcond graph is correct
