A horizontal asymptote is a horizontal line to which the graph of a function appears to approach as the value of (x) becomes extremely large or extremely small. It is denoted by the equation (y = k) where either (\lim_{{x \to \infty}} f(x) = k) or (\lim_{{x \to -\infty}} f(x) = k). The horizontal asymptote is used to determine the end behavior of the function. A function may or may not have a horizontal asymptote, but the maximum number of asymptotes that a function can have is 2. The rules for finding horizontal asymptotes vary for different types of functions, such as rational functions and polynomial functions
. For rational functions, the rules for finding horizontal asymptotes are as follows:
- If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is (y = 0).
- If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and denominator.
- If the degree of the numerator is greater than the degree of the denominator, the rational function has no horizontal asymptote
It's important to note that a function doesn't necessarily have a horizontal asymptote, and the maximum number of asymptotes a function can have is 2
