Question

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

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

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

Answer 1

To understand the transformation that occurs when changing the equation from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \), we can analyze the effect of the "+4" in the equation.

1. **Original function:**
\[
f(x) = -|x|
\]
This is a V-shaped graph that opens downwards, with its vertex at the origin (0, 0).

2. **Transformed function:**
\[
f(x) = -|x| + 4
\]
Here, the "+4" shifts the entire graph vertically.

When you add a constant to a function, it results in a **vertical shift**. In this case, adding 4 means that every point on the graph of \( f(x) = -|x| \) is shifted upward by 4 units.

Thus, the correct description of the transformation is:

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