Afunction, h(x), is defined as shown. h(x) = which graph represents h(x)? {image attached)

The second one! The others do not follow the piecewise function stated.

option B

Step-by-step explanation:

We have three different function for h(x)

WE have x

Plug in 0 for x

So h(0)= -4

When x=0, y= -4

The graph starts at (0,-4) and goes down

x lies between 0  and 3, so the graph starts at x=0 and ends at x=3

Plug in 0 for x

So h(0)= -3

When x=0, y= -4

Plug in 3 for x

When x=3, y= -2

The graph starts at (0,-4) and ends at (3, -2)

WE have x>=4, so the graph starts at x=4 and goes to the right

Plug in 4 for x

So h(4)= 0

When x=4, y= 0

The graph starts at (4,0) and goes to the right.

SEcond graph is correct

given: for the given function h(x), we have given four conditions  

(i) h(x) = (x ÷4) - 4   when x ≤ 0  

here, if x = 0, -1 , -2, -3, -4 then h(x) = -4, -4.25, -4.50, -4.75, -5  

from the above data, it represents the bottom line of the 2nd graph. (ii)   h(x) = (x ÷3) - 3   when   0

here, if x = 1, 2, 3   then h(x) = - 2.7, - 2.3, - 2.0  

from the above data, it represents the second last bottom line of the 2nd graph.

(iii) h(x) = (x ÷2) - 2   when   x ≥ 4  

here, if x = 4, 5, 6, 7 h(x) = 0, 0.5, 1.0,  

from the above data, it represents the top line of the 2nd graph.  

hence, the correct representation of the given function will be the second graph.

The correct answer on edgenuity is graph b