Describe the transformation that occurs on a graph when changing an equation from f(x)=−|x|

Question

𝑓
(
𝑥
)
=
−
|
𝑥
|
to f(x)=−|x|+4
𝑓
(
𝑥
)
=
−
|
𝑥
|
+
4
.(1 point)
Responses

The original function shifts vertically up four units.
The original function shifts vertically up four units.

The original function shifts vertically down four units.
The original function shifts vertically down four units.

The original function shifts horizontally to the left four units.
The original function shifts horizontally to the left four units.

The original function shifts horizontally to the right four units.
The original function shifts horizontally to the right four units.

Answer 1

The transformation that occurs when changing the equation from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \) is that the original function shifts vertically up four units.

This is because adding a constant (+4) to the function shifts the graph upward by that amount, while the rest of the function remains unchanged.