The funcation y = x2 + 2 undergoes a reflection. Which of the following could NOT represent f ' (x), the image of f after the reflection?(1 point) Responses y = x2−4x + 5 y = x2−4x + 5 y =− x2 y =− x2 y = x2 y = x2 160

Answer 1

To determine which function could NOT represent \( f'(x) \), the image of \( f(x) = x^2 + 2 \) after reflection, we should consider what reflection could mean in this context.

1. Reflection over the x-axis: This would change the function to its negative, that is \( f'(x) = -f(x) = - (x^2 + 2) = -x^2 - 2 \).

2. Reflection over the y-axis: This would change the function to \( f'(x) = f(-x) = (-x)^2 + 2 = x^2 + 2 \), which is the same as the original function.

Given the options provided:

1. \( y = x^2 - 4x + 5 \)
2. \( y = -x^2 \)
3. \( y = x^2 \)

• The first option, \( y = x^2 - 4x + 5 \), is a quadratic function that is a transformation of \( x^2 \) (having a vertex at \( (2, 1) \)). It is not a direct reflection of the original function.
• The second option, \( y = -x^2 \), represents a reflection of \( f \) over the x-axis.
• The third option, \( y = x^2 \), represents no change (reflection over the y-axis).

Therefore, the function that could NOT represent \( f'(x) \) after the reflection is:

y = x^2 - 4x + 5