Asymptotes
Asymptotes are lines that a curve approaches but never touches. In other words, they are lines that a function gets infinitely close to as the input values (or variables) approach certain values.
There are two types of asymptotes:
1. Vertical asymptotes: These are vertical lines that a function approaches as the input values approach a certain value. A vertical asymptote occurs when the denominator of a fraction approaches zero or when a function is undefined at a certain value of the input.
2. Horizontal asymptotes: These are horizontal lines that a function approaches as the input values become very large or very small. A horizontal asymptote can occur if the function becomes increasingly close to a constant value as the input values approach infinity or negative infinity.
It's worth noting that not all functions have asymptotes, and some functions may have both vertical and horizontal asymptotes. Asymptotes are important in understanding the behavior of functions and can be useful in applications such as calculus and engineering.
asymptotes | (x^2 - 4)/(x^4 - x)
(x^2 - 4)/(x^4 - x)->0 as x-> ± ∞
(x^2 - 4)/(x^4 - x)-> ± ∞ as x->0
(x^2 - 4)/(x^4 - x)-> ± ∞ as x->1
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