Horizontal Asymptote Finder
Easily find the horizontal asymptotes of rational functions online. Enter your function and get step-by-step solutions and interactive graphs.
Enter a function in the format p(x)/q(x), where p(x) and q(x) are polynomials.
Function Visualization
Understanding Horizontal Asymptotes
A horizontal asymptote is a horizontal line that the graph of a function approaches as x tends to positive or negative infinity. For rational functions (functions in the form of a ratio of two polynomials), horizontal asymptotes are determined by comparing the degrees of the polynomials in the numerator and the denominator.
- 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 y = (leading coefficient of numerator) / (leading coefficient of denominator).
- If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote (but there might be an oblique asymptote).
This tool helps you quickly find the horizontal asymptote for any given rational function and visualize it on a graph. Simply input your function in the specified format and click 'Calculate'.
For more in-depth information, you can refer to resources like Khan Academy's lesson on Horizontal Asymptotes or your calculus textbook.