what are the x-intercepts of f(x)=x+11/x-12

To find the x-intercepts of the function \( f(x) = \frac{x + 11}{x - 12} \), we need to determine where the function equals zero. The x-intercepts occur when \( f(x) = 0 \).

1. Set \( f(x) = 0 \):
   \[
   \frac{x + 11}{x - 12} = 0
   \]

2. For a fraction to be zero, the numerator must be zero. Therefore, we solve:
   \[
   x + 11 = 0
   \]

3. Solving for \( x \):
   \[
   x = -11
   \]

Thus, the x-intercept is at \( x = -11 \). 

### Summary:
- The function \( f(x) \) has an x-intercept at \( x = -11 \).

Would you like further details or have any questions about the process?

Here are 5 related questions:
1. How do we find the y-intercept of this function?
2. What are the vertical asymptotes of the function?
3. Can this function have horizontal asymptotes?
4. How does the function behave near the asymptote at \( x = 12 \)?
5. How do we graph the function step by step?

**Tip:** When analyzing rational functions, always check for points where the denominator equals zero for vertical asymptotes.

Learn how to find the x-intercepts of the rational function f(x) = (x + 11) / (x - 12) with a detailed step-by-step solution. This problem involves key algebraic concepts, including rational functions and solving for x-intercepts. Suitable for students in Grades 9-11.

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