​F(x)equals=StartFraction 1 Over 9 x minus 8 EndFraction
1
9x−8

The function you've written is:

\[
F(x) = \frac{1}{9x - 8}
\]

This is a rational function, where the denominator is \(9x - 8\). Let's break it down:

1. **Domain:** 
   The function is undefined where the denominator is zero. So, to find where the function is undefined, we solve:

   \[
   9x - 8 = 0 \quad \Rightarrow \quad x = \frac{8}{9}
   \]

   Therefore, the domain of the function is all real numbers **except** \(x = \frac{8}{9}\).

2. **Asymptotes:**
   - **Vertical asymptote:** The vertical asymptote occurs where the denominator equals zero, which is at \(x = \frac{8}{9}\).
   - **Horizontal asymptote:** Since the degree of the polynomial in the denominator is higher than in the numerator, the horizontal asymptote is at \(y = 0\).

Would you like to go into further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the range of the function \(F(x) = \frac{1}{9x - 8}\)?
2. How do you find the intercepts (x-intercept and y-intercept) of this function?
3. How do you determine the behavior of the function as \(x \to \infty\)?
4. How would this function change if the numerator was something other than 1, such as \(x\)?
5. Can you graph the function \(F(x)\)? What does the graph look like?

**Tip:** When dealing with rational functions, always check for values that make the denominator zero to determine any restrictions in the domain.

F(x) equals StartFraction 1 Over 9x - 8 EndFraction

Explore the rational function F(x) = 1 / (9x - 8), focusing on finding its domain, vertical and horizontal asymptotes, and other key concepts. This problem is suitable for high school students (Grades 10-12) learning about rational functions and their properties.

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