The function f(x)=x2−1 is reflected over the y-axis. Choose the equation that correctly identifies g(x).

Question

A. g(x)=x2−1
B. g(x)=−x2−2
C. g(x)=−x2+1
D. g(x)=x2+1

Answer 1

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

Starting with the original function: \[ f(x) = x^2 - 1 \]

We reflect it over the y-axis: \[ g(x) = f(-x) = (-x)^2 - 1 \] Since \((-x)^2 = x^2\), we have: \[ g(x) = x^2 - 1 \]

Thus, the equation that identifies \( g(x) \) after the reflection is: \[ g(x) = x^2 - 1 \]

The correct answer is: A. \( g(x) = x^2 - 1 \)