Asymptotes

Asymptotes are lines that a graph of a function approaches but never actually touches or crosses, as you move towards infinity or a certain point. Think of them as boundaries that the graph gets closer to but doesn’t intersect. Vertical asymptotes occur where the function’s value skyrockets or drops sharply, often due to division by zero. Horizontal asymptotes show the long-term behavior of the graph as x becomes very large or very small, indicating a stable value the function approaches. Overall, asymptotes help us understand the end behavior and limits of a graph, providing insight into its long-term tendencies.