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 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.

Answer 1

The correct response is:

The original function shifts vertically up four units.

However, this appears to be an error in your options. The transformation from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \) actually shifts the graph vertically up four units.

To clarify:

• The term \( +4 \) in the equation \( f(x) = -|x| + 4 \) moves the graph of the original function \( f(x) = -|x| \) up by 4 units.

So the proper description is that the graph shifts vertically up four units.