Part 2/6:
To visualize a vertical asymptote, one can consider a function that never actually reaches a specific vertical line, say ( x = a ). Instead, the function gets indefinitely close, creating the asymptote at that line. For instance, certain functions can approach a value but will always remain just outside it, making this concept straightforward yet profound.
Horizontal Asymptotes Explained
While vertical asymptotes deal with behavior at specific points, horizontal asymptotes account for values as ( x ) approaches both positive and negative infinity. These can be defined as:
[
\lim_{{x \to \pm\infty}} f(x) = L
]