Question

Reflect the function f(x)=(x+1)^2 about the origin. What position of the point (-4,9) reflected function
The point (-4,9) reflects to (__,__) in -f(-x)

Answer 1

To reflect the function \( f(x) = (x + 1)^2 \) about the origin, we first need to transform the function accordingly. Reflecting around the origin means we take \( f(-x) \) and multiply it by -1.

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

2. **Now negate this function**:
\[
-f(-x) = - (1 - x)^2
\]

3. **Now let's determine the coordinates of the reflection of the point (-4, 9)**:
- The original point is \((-4, 9)\).
- The reflection across the origin involves taking both coordinates and negating them.

Hence, reflecting the point:
\[
(-4, 9) \rightarrow (4, -9)
\]

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

Therefore, the answer is:
\[
(4, -9)
\]