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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).

1 answer

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 \((4, 3)\).