Question

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

g(x)=x2+1
g left parenthesis x right parenthesis equals x squared plus 1

g(x)=−x2−2
g left parenthesis x right parenthesis equals negative x squared minus 2

g(x)=−x2+1
g left parenthesis x right parenthesis equals negative x squared plus 1

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 \( -x \).

When we do that, we get:

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

So, the reflection of \( f(x) \) over the y-axis gives us:

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

Therefore, the correct equation for \( g(x) \) is:

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

From the provided options, the correct choice is:

**g(x) = x² - 1**.