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 graph at extreme values (like very large or very small x or y). 2. There are three main types of asymptotes: - **Vertical asymptotes** occur where the function goes to infinity or negative infinity as x approaches a certain value. - **Horizontal asymptotes** show the value that the function approaches as x goes to positive or negative infinity. - **Oblique (slant) asymptotes** happen when the graph approaches a line that is neither vertical nor horizontal. 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** of a function is the set of all possible output values (y-values) that the function can produce. 5. To summarize: - **Asymptotes** describe the behavior of the graph near certain lines. - **Domain** tells us which x-values we can plug into the function. - **Range** tells us what y-values the function can output. Understanding these concepts helps us analyze and graph functions more effectively.