Reflect the function f(x)=(x+1)2

Question

Reflect the function  f(x)=(x+1)2
  about the origin. What is the position of the point  (−4,9)
  in the reflected function?(1 point)
The point (−4,9)
 reflects to (
,
) in −f(−x)
.
Remaining Attempts : 3

GPT-4o mini · Answer

To reflect the function $ f(x) = (x + 1)^2 $ about the origin, we first need to find the equation of the reflected function. The reflection of a function $ y = f(x) $ about the origin is given by $ y = -f(-x) $. 1. First, we find $ -f(-x) $: $$ f(-x) = (-x + 1)^2 = (1 - x)^2 $$ Now we apply the negative: $$ -f(-x) = -(1 - x)^2 $$ 2. Now we need to calculate the position of the point $(-4, 9)$ under this reflection. The point we have is $ (-4, 9) $, which means $ x = -4 $ and $ f(-4) = 9 $. 3. First, we reflect the x-coordinate: $$ x' = -(-4) = 4 $$ 4. Now, we substitute $ x = 4 $ into the original function to find the corresponding y-coordinate: $$ f(4) = (4 + 1)^2 = 5^2 = 25 $$ So, plugging it into the reflected function gives: $$ y' = -f(-4) = -9 $$ 5. Therefore, the point $(-4, 9)$ reflects to $(4, -9)$ in the reflected function $ -f(-x) $. Thus, the answer is: The point $(-4, 9)$ reflects to $(4, -9)$ in $-f(-x)$.