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You are asked to determine whether the given function is continuous.

The function is \( f(x) = \frac{5}{x + 2} \), and you are asked to determine continuity over the interval (6, 10).

### Steps to Check Continuity:

1. **Domain of the Function**:
   - The function \( f(x) = \frac{5}{x + 2} \) is a rational function, and rational functions are continuous everywhere in their domain. 
   - The domain is restricted where the denominator is zero. Therefore, we set \( x + 2 = 0 \), which gives \( x = -2 \).
   - So, \( f(x) \) is undefined at \( x = -2 \), meaning the function is **discontinuous** only at \( x = -2 \).

2. **Interval (6, 10)**:
   - The interval given is (6, 10), which does not include \( x = -2 \).
   - Therefore, \( f(x) = \frac{5}{x + 2} \) is continuous over the interval (6, 10), because it does not contain the point where the function is undefined.

### Conclusion:
The function \( f(x) = \frac{5}{x+2} \) is continuous on the interval (6, 10).

Would you like more details or have any questions?

### Related Questions:
1. What is the domain of a rational function?
2. How do you check for points of discontinuity in a function?
3. What is the formal definition of continuity for a function?
4. How do you determine continuity over an open interval?
5. How do vertical asymptotes affect the continuity of a function?

### Tip:
When working with rational functions, always check where the denominator equals zero, as these are the points where the function may be discontinuous.

Determine whether the function f(x) = 5 / (x + 2) is continuous on the interval (6, 10).

Learn how to determine whether the function f(x) = 5 / (x + 2) is continuous over the interval (6, 10). This problem involves understanding the domain of rational functions and checking for points of discontinuity. Suitable for high school students in Grades 10-12.

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