Rational functions and graphs

Rational functions and asymptotes

A rational function $y=\frac{P(x)}{Q(x)}$ has vertical asymptotes where $Q(x)=0$, and its behaviour for large $|x|$ (horizontal or oblique asymptote) comes from dividing. Writing $y=f(x)$ as a quadratic in $x$ and using the discriminant gives the range and turning points.