1. **Problem Statement:** Explain in simple words what an asymptote means. 2. **Definition:** An asymptote is a line that a graph of a function gets closer and closer to but never actually touches or crosses as the input values become very large or very small. 3. **Explanation:** Imagine you are walking towards a wall but you keep halving the distance each step. You get closer and closer but never actually reach the wall. That wall is like an asymptote. 4. **Types:** There are different types of asymptotes: - Horizontal asymptotes: The graph approaches a horizontal line as $x$ goes to $\pm \infty$. - Vertical asymptotes: The graph shoots up or down near some $x$ value where the function is undefined. - Oblique asymptotes: The graph approaches a slanted line. 5. **In our function:** For $f(x) = \frac{x^2}{x^2 + 4}$, the horizontal asymptote is $y=1$ because as $x$ becomes very large or very small, $f(x)$ gets closer to 1 but never equals it. **Final answer:** An asymptote is a line that the graph of a function approaches but never touches, showing the behavior of the function at extreme values of $x$.