Question

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

Answer 1

To reflect the function \( f(x) = x + 1 \) about the origin, we need to transform the function into \(-f(-x)\).

### Step 1: Find \(-f(-x)\)

1. Substitute \(-x\) into the function:
\[
f(-x) = -x + 1
\]

2. Now apply the negative sign:
\[
-f(-x) = -(-x + 1) = x - 1
\]

So, the reflected function is \( g(x) = x - 1 \).

### Step 2: Find the new position of the point (-4, 9)

To find where the point \((-4, 9)\) reflects to under the new function \(g(x)\):

1. First, determine the x-coordinate of the reflection:
\[
x = 4 \quad \text{(since reflection over the origin flips the sign of both coordinates)}
\]

2. Now, calculate \(g(4)\):
\[
g(4) = 4 - 1 = 3
\]

### Conclusion

The reflected point of \((-4, 9)\) in the function \(g(x)\) is:
\[
(4, 3)
\]

Thus, the position of the point \((-4, 9)\) in the reflected function is \((4, 3)\).