Question

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

Answer 1

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

Answer 2

Answer:

option B

Step-by-step explanation:

We have three different function for h(x)

$h(x)= \frac{1}{4}x-4, x$

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

Plug in 0 for x

$h(0)= \frac{1}{4}(0)-4$

So h(0)= -4

When x=0, y= -4

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

$h(x)= \frac{1}{3}x-3, 0$

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

Plug in 0 for x

$h(0)= \frac{1}{3}(0)-3$

So h(0)= -3

When x=0, y= -4

Plug in 3 for x

$h(3)= \frac{1}{3}(3)-3=-2$

When x=3, y= -2

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

$h(x)= \frac{1}{2}x-2, x>=4$

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

Plug in 4 for x

$h(4)= \frac{1}{2}(4)-2$

So h(4)= 0

When x=4, y= 0

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

SEcond graph is correct