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

Question

Graph the function  f(x)=(x+1)2
  and the function of its horizontal reflection. What is the position of the point  (−4,9)
  in the reflected function?(1 point)
The point (−4,9)
  reflects to (
) in f(−x)
.
Re

GPT-4o mini · Answer

To reflect the function $ f(x) = (x+1)^2 $ horizontally, we will replace $ x $ with $ -x $. Thus, the reflected function is: $$ f(-x) = (-x + 1)^2 = (1 - x)^2. $$ Now let's analyze the behavior of both functions and determine the position of the point $ (-4, 9) $ in the reflected function. 1. **Original Function:** Let's calculate $ f(-4) $: $$ f(-4) = (-4 + 1)^2 = (-3)^2 = 9. $$ So, the point $ (-4, 9) $ is on the original function $ f(x) $. 2. **Reflected Function:** Now, we want to find the equivalent point in the reflected function $ f(-x) $. The point $ (-4, 9) $ reflects to the point $ (4, 9) $ in the equation $ f(-x) $. Thus, the position of the point $ (-4, 9) $ in the reflected function $ f(-x) $ is: $$ (4, 9). $$ In conclusion, the point $ (-4, 9) $ reflects to $ (4, 9) $ in $ f(-x) $.