Graphs:
Need maxima and minima (y'=0, relative or absolute), inflection
points (y''=0), vertical asymptotes ( finite),
horizontal asymptotes (
finite), oblique asymptotes
(
), behavior at infinity (
),
intercepts (x or y=0), singular points (corners, cusps, crossings,
infinite curvature, ...), concavity (upward if y''>0), symmetry
or anti-symmetry around x, y, or general oblique axes, ...)
See page 133 in the 4th edition of Ayres.
If you can, draw the curve first, then fill in the details.