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)

Answer 1

To graph the function \( f(x) = (x + 1)^2 \) and its horizontal reflection \( f(-x) \), let's first determine each function.

1. **Original Function:**
\[
f(x) = (x + 1)^2
\]
This is a parabola that opens upwards, with its vertex at the point \( (-1, 0) \).

2. **Horizontal Reflection:**
The horizontal reflection of a function \( f(x) \) is obtained by replacing \( x \) with \( -x \). So, we have:
\[
f(-x) = (-x + 1)^2 = (1 - x)^2
\]
This is also a parabola opening upwards, with its vertex at the point \( (1, 0) \).

Now, let's find the point that corresponds to the point \( (-4, 9) \) in the reflected function \( f(-x) \).

To reflect the point \( (-4, 9) \) over the y-axis:
- The x-coordinate will change sign, so the reflected point will be \( (4, 9) \).

Now, we need to check if this reflected point is actually on \( f(-x) \):
- Substitute \( x = 4 \) into \( f(-x) \):
\[
f(-4) = (1 - (-4))^2 = (1 + 4)^2 = 5^2 = 25
\]

Thus, the point \( (4, 9) \) does **not** lie on \( f(-x) \), as \( f(-4) = 25 \).

In conclusion, the reflection of the point \( (-4, 9) \) in the context of the reflected function \( f(-x) \) is:
\[
\text{The point (-4, 9) reflects to (4, 9) in } f(-x).
\]