Question

Find g (x), which is a reflection over the y-axis of f (x) = x^2 - x.

a. g (x) = -x^2 + 7x
b. g (x) = -x^2 + x
c. g (x) = 6x^2
d. g (x) = x^2 + x

Answer 1

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

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

Calculating \( f(-x) \):

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

So, we have:

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

From the options provided, the correct answer is:

d. \( g(x) = x^2 + x \)