1. Let's start by defining the **asymptote**. An asymptote is a line that a graph approaches but never actually touches or crosses. It shows the behavior of the function as the input values become very large or very small. 2. There are different types of asymptotes: vertical, horizontal, and oblique (slant). Vertical asymptotes occur where the function is undefined and the values go to infinity. Horizontal asymptotes show the value the function approaches as $x$ goes to infinity or negative infinity. 3. Now, the **domain** of a function is the set of all possible input values ($x$ values) for which the function is defined. For example, if a function has a denominator, the domain excludes values that make the denominator zero. 4. The **range** is the set of all possible output values ($y$ values) that the function can produce. It depends on the behavior of the function and its domain. 5. To summarize: - **Asymptote:** A line the graph approaches but never touches. - **Domain:** All valid input values. - **Range:** All possible output values. 6. Understanding these concepts helps us analyze and graph functions effectively.