Question

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

a. g (x) = x^2 + 1
b. g (x) = x^2 - 1
c. g (x) = -x^2 + 1
d. g (x) = x^2 - 2

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.

So, we have:

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

Calculating this gives:

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

Now, we compare this with the options provided:

a. \( g(x) = x^2 + 1 \)

b. \( g(x) = x^2 - 1 \)

c. \( g(x) = -x^2 + 1 \)

d. \( g(x) = x^2 - 2 \)

The correct choice that matches our derived equation \( g(x) = x^2 - 1 \) is:

**b. \( g(x) = x^2 - 1 \)**.