Question

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

g(x)=−x2+x
g left parenthesis x right parenthesis equals negative x squared plus x

g(x)=−(x2−x)
g left parenthesis x right parenthesis equals negative left parenthesis x squared minus x right parenthesis

g(x)=−x2−x
g left parenthesis x right parenthesis equals negative x squared minus x

g(x)=x2+x

Answer 1

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

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

Now, let's compute \( g(x) = f(-x) \):
\[
g(x) = (-x)^2 - (-x)
\]
\[
g(x) = x^2 + x
\]

Thus, the reflection of \( f(x) \) over the y-axis is:
\[
g(x) = x^2 + x
\]

The correct response is:
\[
g(x) = x^2 + x
\]