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

Question

to f(x)=−|x|+4
.(1 point)
Responses

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

The original function shifts vertically up four units

Answer 1

When changing the equation from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \), the transformation is a vertical shift.

Specifically, the graph of \( f(x) = -|x| + 4 \) shifts vertically up by 4 units compared to the graph of \( f(x) = -|x| \).

So, the correct response is:

The original function shifts vertically up four units.