A function, h(x), is defined as shown.h(x) = Which graph represents h(x)? {image Attached)

Answer:option BStep-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 downPlug in 0 for x[tex]h(0)= \frac{1}{4}(0)-4[/tex]So h(0)= -4When x=0, y= -4The 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=3Plug in 0 for x[tex]h(0)= \frac{1}{3}(0)-3[/tex]So h(0)= -3When x=0, y= -4Plug in 3 for x[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]When x=3, y= -2The 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 rightPlug in 4 for x[tex]h(4)= \frac{1}{2}(4)-2[/tex]So h(4)= 0When x=4, y= 0The graph starts at (4,0) and goes to the right.SEcond graph is correct