The function you provided is:

$F(x) = \frac{1}{x - 2} + 3$

This is a rational function where the variable $x$ appears in the denominator of the first term. Let's break it down:

1. The term $\frac{1}{x - 2}$ represents a rational function with a vertical asymptote at $x = 2$ (because the denominator becomes zero at $x = 2$, which makes the function undefined).
2. The constant $+3$ shifts the entire graph of the function upwards by 3 units.

Key features of the function:

• Vertical asymptote: at $x = 2$.
• Horizontal asymptote: Since the constant term is $+3$, the horizontal asymptote is $y = 3$, because as $x$ becomes very large or very small, $\frac{1}{x - 2}$ approaches 0.
• Domain: All real numbers except $x = 2$, i.e., $(-\infty, 2) \cup (2, \infty)$.

Would you like to go into further details or clarify any part of this?

Here are 5 related questions to expand this concept:

1. How would the graph change if we altered the constant 3 to another number?
2. What is the behavior of the function as $x \to 2$ from the left and right sides?
3. Can we calculate the derivative of this function?
4. How would you find the x-intercept of this function?
5. What is the effect of modifying the denominator to $x - a$ instead of $x - 2$?

Tip: For rational functions like these, always identify vertical and horizontal asymptotes, as they provide key information about the function's behavior.