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

Question

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)
.

Answer 1

To reflect the function \( f(x) = (x + 1)^2 \) across the y-axis, we replace \( x \) with \( -x \). This gives us the reflected function:

\[ f(-x) = (-x + 1)^2 = (1 - x)^2 \]

Now, let's determine the position of the point \((-4, 9)\) in the reflected function \( f(-x) \).

1. First, we need to find the corresponding x-value in the reflected function:

   • The x-coordinate of the original point is \( -4 \).
   • For the reflected function, we use \( -x \), so we find \( x \) such that \( -x = -4 \), which gives \( x = 4 \).

2. Next, we calculate \( f(-4) \) in the reflected function \( f(-x) \): \[ f(4) = (1 - 4)^2 = (-3)^2 = 9 \]

So, in the reflected function \( f(-x) \), the point corresponds to the coordinates \( (4, 9) \).

Thus, the point \((-4, 9)\) reflects to \((4, 9)\) in \( f(-x) \).

Final Answer: (4, 9)