Rational functions

A rational function is any function which can be defined by a rational fraction where both the numerator and denominator are polynomials. To graph a rational function, you aphave to first find the asymptotes and the intercepts. Then from that, you have to plot the plots then graph. The vertical asymptote can be found by setting the denominator equal to zero and the solving for x. Once the asymptotes are drawn on the graph, it means that the function cannot touch that line so the graph would maneuver around it. The horizontal asymptote can be found by comparing the exponents of the variables. So the largest variable in the numerator is compared to that if the denominator by following a set of rules. If n<m, n being the numerator, then the x-axis is the horizontal aymptote. If it is the opposite, the there is no horizontal asymptote and instead you would find a slant asymptote. If n=m, then the horizontal asymptote is y=a/b.