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.