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Descarte's Rule of Signs: Let f(x) define a polynomial function with real coefficients and a nonzero constant term, with terms in descending powers of x

- the number of positive real zeros of f either equals the number of variations by a positive even integer
- the number of negative real zeros of f either equals the number of variations in sign occurring in the coefficients of f(-x), or is less than the number of variations by positive even integer.

Steps to graph:

- factor completely
- find and plot the zeros (on x axis)
- determine the end behavior
- determine multiplicity of each zero

Polynomial graphs:

- unless restricted, the domain is (-infinity, infinity)
- graphs are smooth, continuous curves
- range: odd function will be (-infinity, infinity); even function will be (-infinity, k] or [k, infinity)

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