Find g(x)

Question

, 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 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 plus x

g(x)=−x2−x

Answer 1

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

So,

$$g(x)=f(-x)=(-x{)}^2-(-x)$$

Calculating that:

$$g(x)=x^2+x$$

Thus, the correct response is:

$$g(x)=x^2+x$$