The given function is:

\[
f(x) = \sqrt{x^2 + 4} - 8
\]

Let's break it down:

1. The expression inside the square root is \(x^2 + 4\).
2. You then take the square root of that expression, resulting in \(\sqrt{x^2 + 4}\).
3. Finally, subtract 8 from that result.

Is there something specific you'd like to do with this function? For example, would you like to find the domain, derivative, or graph it?

### Follow-up questions:
1. What is the domain of \( f(x) \)?
2. How do you differentiate \( f(x) \)?
3. What is the range of \( f(x) \)?
4. How would you solve \( f(x) = 0 \)?
5. What is the behavior of \( f(x) \) as \( x \to \infty \)?

**Tip:** To differentiate square roots, use the chain rule and treat the square root as an exponent.

Explore the function f(x) = √(x^2 + 4) - 8 with a detailed breakdown of its domain, range, and derivative. This algebraic problem covers important concepts like square roots, the chain rule for differentiation, and behavior analysis as x approaches infinity. Suitable for Grades 10-12.

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