Michigan Algebra I Sept. 2012

The end behavior of polynomials is as follows:

For even degree polynomials, with a positive leading coefficient,

• as x approaches infinity, f(x) or y approaches infinity
• and as x approaches negative infinity, f(x)or y approaches infinity

For odd degree polynomials, with a positive leading coefficient,

• as x approaches infinity, f(x) approaches infinity
• and as x approaches negative infinity, f(x) approaches negative infinity

Polynomials with negative leading coefficients will have the opposite end behaviors. For example, odd degree polynomials with a negative leading coefficient,

• as x approaches infinity, f(x) approaches negative infinity
• and as x approaches negative infinity, f(x) approaches positive infinity