Question

The function f (x) is a parabola in the standard (x, y)
coordinate plane. Which of the following transformed
functions shifts f (x) over 2 units to the right and down 4
units?

A.
f (x + 2) – 4
B.
f (x + 2) + 4
C.
f (x – 2) – 4
D.
f (x – 4) + 2
E.
f (x + 4) – 2

Answer 1

To shift a function \( f(x) \) horizontally and vertically, we need to adjust the input \( x \) and the output \( f(x) \) accordingly.

1. **Shifting 2 units to the right**: To move the function to the right, we replace \( x \) with \( x - 2 \). Thus, the transformed function would look like \( f(x - 2) \).

2. **Shifting down 4 units**: To move the function down, we subtract 4 from the entire function. Therefore, the function would look like \( f(x - 2) - 4 \).

Putting both transformations together, the transformation that shifts \( f(x) \) over 2 units to the right and down 4 units is given by:

\[
f(x - 2) - 4
\]

Now, let’s compare this with the provided options:

A. \( f(x + 2) - 4 \)

B. \( f(x + 2) + 4 \)

C. \( f(x - 2) - 4 \)

D. \( f(x - 4) + 2 \)

E. \( f(x + 4) - 2 \)

The correct answer is:

**C. \( f(x - 2) - 4 \)**