The function f (x) = x^2 - 1 is reflected over the y-axis. Choose the equation that correctly identifies g(x).

1 answer

To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we replace \( x \) with \( -x \) in the function.

So, the equation for the reflected function \( g(x) \) is:

\[ g(x) = f(-x) = (-x)^2 - 1 \]

Now, simplifying this gives:

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

Thus, the equation that correctly identifies \( g(x) \) after reflecting \( f(x) \) over the y-axis is:

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

This means that reflecting \( f(x) \) over the y-axis does not change the function since it is an even function.