A horizontal asymptote is a straight line that a graph approaches but never touches as the input value increases or decreases without bound. It is often referred to as the "end behavior" of a function.
To determine the horizontal asymptote of a function, you need to look at the highest degree terms in the numerator and denominator of the function. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
No, a function can only have at most one horizontal asymptote. This is because the end behavior of a function is determined by the highest degree terms in the numerator and denominator, and there can only be one highest degree term in each.
The horizontal asymptote of a function can provide important information about the behavior of the function. It can help determine the range of the function, whether it is increasing or decreasing, and whether it has any intercepts.
No, a function cannot cross its horizontal asymptote. The asymptote represents the limit of the function as the input value approaches infinity or negative infinity, and the function cannot cross this limit.
