To reflect the function \( f(x) = (x + 1)^2 \) horizontally, we need to replace \( x \) with \( -x \). The horizontally reflected function is \( f(-x) = (-x + 1)^2 = (1 - x)^2 \).
Next, we analyze the position of the point \( (-4, 9) \) in the original function:
- Calculate if the point \( (-4, 9) \) lies on \( f(x) \): \[ f(-4) = (-4 + 1)^2 = (-3)^2 = 9 \] So, indeed, \( (-4, 9) \) lies on the graph of \( f(x) \).
Now we need to find the reflection of the point \( (-4, 9) \) in the reflected function \( f(-x) \):
- To reflect this point, we simply take the x-coordinate and negate it: \[ (-4, 9) \rightarrow (4, 9) \]
Thus, the position of the point \( (-4, 9) \) in the reflected function \( f(-x) \) is: \[ (4, 9) \]
So, the answer is: \[ (4, 9) \]