To sketch a polynomial function:
 · Note the degree of the polynomial
  use it to predict the general shape and end behavior.
  even functions "start high & end high"
  odd functions "start low & end high"

 · Note the coefficient of the term with highest degree
  use it to determine if the curve is reflected about the xaxis.
 x³ "starts low and ends high"
 (generally increases as x increases)
  x³ "starts high and ends low"
 (generally decreases as x increases)

 · Rewrite it by factoring
 identify the linear, quadratic, or other factors.
 · Plot the real zeros.
 · Note for each root or zero what kind of a root it is
  odd powers pass through the xaxis,
  even powers touch but do not pass through the xaxis.

 · Plot (0, f(0)), the yintercept.
 · Solve: first derivative = 0
  to find relative maximums/minimums.
 · Determine sign in intervals
  using the positiveness or negativeness of each factor.
  just "connect the dots."
 · Sketch curve.
