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

1 answer

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

Starting with the function: \[ f(x) = \frac{1}{-x^2} + x \]

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

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

Thus, the final expression for the reflected function \( g(x) \) is: \[ g(x) = \frac{1}{-x^2} - x \]

In the form you provided, to fill in the blanks: \[ G(x) = \frac{1}{-x^2} + (-1)x \]

So, the completed expression would be: \[ G(x) = \frac{1}{-x^2} - x \]

Therefore, the answers to fill in the blanks are:

  • The blank for the first term: \(-\)
  • The blank for the second term: \(-1\)