Question

Find g(x), which is a reflection over the y-axis of f(x)= x2 − x.(1 point)
Responses

g(x) = 6x2 g(x) = 6x2

g(x) = −x2 + xg(x) = −x2 + x

g(x) = −x2 + 7xg(x) = −x2 + 7x

g(x) = x2 + x

Answer 1

To find \( g(x) \), which is the reflection of \( f(x) = x^2 - x \) over the y-axis, we need to replace \( x \) with \( -x \) in the function \( f(x) \).

Starting with:
\[
f(x) = x^2 - x
\]

We replace \( x \) with \( -x \):
\[
g(x) = f(-x) = (-x)^2 - (-x)
\]

Calculating this gives:
\[
g(x) = x^2 + x
\]

So the reflection over the y-axis is:
\[
g(x) = x^2 + x
\]

Therefore, the correct response is:
\[
\boxed{g(x) = x^2 + x}
\]