Question

A function, h(x), is defined as shown.

h(x) =

Which graph represents h(x)? {image Attached)

Answer 1

B

Explanation:

Answer 2

option B

Explanation:

We have three different function for h(x)

`h(x)= (1)/(4)x-4, x<=0`

WE have x<=0, so the graph starts at x=0 and goes down

Plug in 0 for x

`h(0)= (1)/(4)(0)-4`

So h(0)= -4

When x=0, y= -4

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

`h(x)= (1)/(3)x-3, 0<x<=3`

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

Plug in 0 for x

`h(0)= (1)/(3)(0)-3`

So h(0)= -3

When x=0, y= -4

Plug in 3 for x

`h(3)= (1)/(3)(3)-3=-2`

When x=3, y= -2

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

`h(x)= (1)/(2)x-2, x>=4`

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

Plug in 4 for x

`h(4)= (1)/(2)(4)-2`

So h(4)= 0

When x=4, y= 0

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

SEcond graph is correct