Asymptote Calculator and Rational Function Grapher
Enter a polynomial on top and a polynomial underneath and this finds the asymptotes of the fraction. It cancels any common factor exactly first, which is what separates a hole in the graph from a vertical asymptote, then reads the vertical asymptotes off the remaining denominator, compares degrees for a horizontal one, and divides top by bottom for a slant one. You also get the domain, the intercepts, which way the curve runs at each pole, and a sketch with the asymptotes drawn in. It reads polynomials in x up to degree six, with brackets and products; trigonometric, exponential, logarithmic and radical functions are outside it.