To sketch a rational function, we need to find the asymptotes, axial intercepts (if any) and turning points (if any).
If the rational function is an improper fraction, change it to a proper fraction.
The Quotient Function, Q(x) gives the curvilinear/oblique/horizontal asymptote.
The Divisor Function, D(x) tells us the vertical asymptotes.
Use the applet below to explore the graphs of rational functions.