Question

Find g(x), which is a reflection over the y-axis of f (x) = x^2 - x.
A. g (x) = 6x^2
B. g (x) = -x^2 + x
C. g (x) = -x^2 + 7x
D. g (x) = x^2 + x

Answer 1

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

So, we have:

\[
g(x) = f(-x) = (-x)^2 - (-x)
\]

Calculating this gives:

\[
g(x) = x^2 + x
\]

Thus, the correct function \( g(x) \) is:

\[
g(x) = x^2 + x
\]

Looking at the answer options, the correct choice is:

**D. g(x) = x^2 + x**