Question

Use the function f(x)=1/-x^2+x to create its reflection g(x) in the coordinate plane over the y axis.
G(x)=1/____x^2 ____x

Answer 1

To find the reflection \( g(x) \) of the function \( f(x) = \frac{1}{-x^2 + x} \) over the y-axis, we need to replace \( x \) with \( -x \) in the original function.

Starting from the function:

\[
f(x) = \frac{1}{-x^2 + x}
\]

We replace \( x \) with \( -x \):

\[
g(x) = f(-x) = \frac{1}{-(-x)^2 + (-x)}
\]

Now, simplify the expression:

\[
g(x) = \frac{1}{-x^2 - x}
\]

So, we can fill in the blanks to get:

\[
g(x) = \frac{1}{-x^2 - x}
\]

Thus, the completed function is:

\[
g(x) = \frac{1}{-x^2 - x}
\]