Question

Reflect the function f(x)=(x+1)2
about the origin. What is the position of the point (−4,9)
in the reflected function?(1 point)
The point (−4,9)
reflects to (
,
) in −f(−x)
.
Remaining Attempts : 3

Answer 1

To reflect the function \( f(x) = (x + 1)^2 \) about the origin, we first need to find the equation of the reflected function.

The reflection of a function \( y = f(x) \) about the origin is given by \( y = -f(-x) \).

1. First, we find \( -f(-x) \):
\[
f(-x) = (-x + 1)^2 = (1 - x)^2
\]
Now we apply the negative:
\[
-f(-x) = -(1 - x)^2
\]

2. Now we need to calculate the position of the point \((-4, 9)\) under this reflection. The point we have is \( (-4, 9) \), which means \( x = -4 \) and \( f(-4) = 9 \).

3. First, we reflect the x-coordinate:
\[
x' = -(-4) = 4
\]

4. Now, we substitute \( x = 4 \) into the original function to find the corresponding y-coordinate:
\[
f(4) = (4 + 1)^2 = 5^2 = 25
\]
So, plugging it into the reflected function gives:
\[
y' = -f(-4) = -9
\]

5. Therefore, the point \((-4, 9)\) reflects to \((4, -9)\) in the reflected function \( -f(-x) \).

Thus, the answer is:
The point \((-4, 9)\) reflects to \((4, -9)\) in \(-f(-x)\).