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

The original function shifts horizontally to the left 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 effects of the "+4" at the end of the equation.

The operation of adding 4 to the function shifts the entire graph vertically. Specifically:

• When you add a positive number to a function, it shifts the graph upward by that number of units.

So, when we go from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \), the graph of the function shifts vertically upwards by 4 units.

Thus, the correct response would be:

The original function shifts vertically up four units.