Describe the transformation that occurs on a graph when changing an equation from f(x)=−|x to f(x)=−|x|+4

Question

Responses

The original function shifts vertically down four units.

The original function shifts horizontally to the left four units.

The original function shifts vertically up four units.

The original function shifts horizontally to the right four units.

Answer 1

To analyze the transformation from the function \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \), we can break it down step by step.

1. The original function \( f(x) = -|x| \) represents a V-shaped graph that opens downward with its vertex at the origin (0,0).

2. The transformation \( f(x) = -|x| + 4 \) means that we are adding 4 to the output of the original function. This results in a vertical shift of the graph.

Since we're adding 4 to the equation, the entire graph of \( f(x) = -|x| \) moves upward by 4 units.

Therefore, the correct response is:

The original function shifts vertically up four units.