To reflect the function \( f(x) = x + 1 \) about the origin, you need to replace \( x \) with \(-x\) and multiply the entire function by -1. So, the reflection about the origin will be:
\[ -f(-x) = -(-x + 1) = x - 1 \]
The reflected function is \( g(x) = x - 1 \).
Next, to find the position of the point (-4, 9) in the reflected function, we can evaluate the reflected function \( g(x) \) at \( x = -4 \):
\[ g(-4) = -4 - 1 = -5 \]
Thus, the reflected point corresponding to the original \( (-4, 9) \) is \( (-4, -5) \).
So, the final answer is that the point \( (-4, 9) \) reflects to \( (-4, -5) \) in the reflected function.
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