Question

Graph the function f(x)=(x+1)2
and the function of its horizontal reflection. What is the position of the point (−4,9)
in the reflected function?(1 point)
The point (−4,9)
reflects to (
) in f(−x)
.
Re

Answer 1

To reflect the function \( f(x) = (x+1)^2 \) horizontally, we will replace \( x \) with \( -x \). Thus, the reflected function is:

\[
f(-x) = (-x + 1)^2 = (1 - x)^2.
\]

Now let's analyze the behavior of both functions and determine the position of the point \( (-4, 9) \) in the reflected function.

1. **Original Function:** Let's calculate \( f(-4) \):

\[
f(-4) = (-4 + 1)^2 = (-3)^2 = 9.
\]

So, the point \( (-4, 9) \) is on the original function \( f(x) \).

2. **Reflected Function:** Now, we want to find the equivalent point in the reflected function \( f(-x) \). The point \( (-4, 9) \) reflects to the point \( (4, 9) \) in the equation \( f(-x) \).

Thus, the position of the point \( (-4, 9) \) in the reflected function \( f(-x) \) is:

\[
(4, 9).
\]

In conclusion, the point \( (-4, 9) \) reflects to \( (4, 9) \) in \( f(-x) \).