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We are given that the function \( f(x) = x^2 - 1 \) is reflected over the y-axis, and we need to determine the equation for \( g(x) \), the reflected function.

### Reflection over the y-axis:
To reflect a function over the y-axis, we replace \( x \) with \( -x \) in the function. This means that the function \( f(x) \) will become:

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

Since \( (-x)^2 = x^2 \), the equation simplifies to:

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

Thus, the reflected function is \( g(x) = x^2 - 1 \).

### Conclusion:
The correct equation is \( g(x) = x^2 - 1 \), which matches the fourth option in the given choices.

Let me know if you'd like further details or have questions.

Here are 5 related questions to expand your understanding:
1. How do you reflect a function over the x-axis?
2. What is the general rule for reflecting functions over the line \( y = x \)?
3. How would you reflect the function \( f(x) = x^2 - 1 \) over the x-axis?
4. What would happen if you shifted the function \( f(x) \) by 2 units to the right?
5. How does the graph of \( g(x) = x^2 - 1 \) compare to \( g(x) = -x^2 - 1 \)?

**Tip:** Whenever reflecting a function over the y-axis, remember to substitute \( x \) with \( -x \).

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

Learn how to reflect the function f(x) = x^2 - 1 over the y-axis and determine the equation for the reflected function g(x). This problem focuses on function reflections and quadratic functions, suitable for students in Grades 8-10.

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