https://file.aiquickdraw.com/mathbot/file/1725981847081z6moyc1a.jpg

The equation from the image is:

\[
y = \frac{\sqrt{x - 2}}{x^2 - 16}
\]

### Key points to analyze:
1. **Domain Restrictions**: The expression inside the square root \((x - 2)\) must be non-negative for real values, so \(x \geq 2\). Additionally, the denominator \((x^2 - 16)\) must not be zero, which occurs when \(x = \pm 4\).

   Therefore, the **domain** of the function is \(x \geq 2\) with \(x \neq 4\).

2. **Denominator Simplification**: The denominator \(x^2 - 16\) can be factored as:
   \[
   x^2 - 16 = (x - 4)(x + 4)
   \]
   This indicates that at \(x = 4\), the function is undefined (there's a vertical asymptote).

### Summary:
The function has a domain of \(x \geq 2\) excluding \(x = 4\), i.e., \(x \in [2, 4) \cup (4, \infty)\).

Would you like to explore the graph of this function, analyze limits, or simplify further?

### Related Questions:
1. What happens to the function as \(x\) approaches \(4\) from both sides?
2. Can you find the horizontal and vertical asymptotes for this function?
3. How would the graph of the function behave as \(x \to \infty\)?
4. Can you differentiate the function to find critical points and analyze its behavior?
5. How would the function behave if the square root were removed or changed to another power?

**Tip**: Always consider both domain and undefined points when analyzing a rational function.

Explore the domain and key features of the function y = sqrt(x - 2) / (x^2 - 16). This problem involves algebraic concepts such as domain restrictions and factoring quadratic expressions. Suitable for students in Grades 10-12.

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