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 $f^{\prime }(x)$, 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 $f^{\prime }(x)=-f(x)=-(x^2+2)=-x^2-2$.

2. Reflection over the y-axis: This would change the function to $f^{\prime }(x)=f(-x)=(-x{)}^2+2=x^2+2$, 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 $f^{\prime }(x)$ after the reflection is:

y = x^2 - 4x + 5