College Algebra 'Descarte's'

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:

1. factor completely
2. find and plot the zeros (on x axis)
3. determine the end behavior
4. 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)