Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions to solve problems.

Polynomial functions are classified by their degree Polynomial functions are classified by their degree. The graphs of polynomial functions are classified by the degree of the polynomial. Each graph, based on the degree, has a distinctive shape and characteristics.

End behavior is a description of the values of the function as x approaches positive infinity (x +∞) goes to the right or negative infinity (x –∞) goes to the left. The degree and leading coefficient of a polynomial function determines its end behavior. It is helpful when you are graphing a polynomial function to know about the end behavior of the function.

END BEHAVIOR – be the polynomial The LEADING COEFFICIENT is either positive or negative Positive, put your right arm up; negative, put your right arm down The DEGREE is either even or odd Even, arms together; odd, arms apart (or opposite)

Determine the end behavior: 1. 4x4 – 2x3 + 6x – 3 = 0 Leading Coefficient → POSITIVE → right arm up Degree → EVEN → arms together

Determine the end behavior: 2. 3x7 + 8x2 + 4x – 13 = 0 Leading Coefficient → POSITIVE → right arm up Degree → ODD → arms apart

Determine the end behavior: 3. -2x5 + x4 - 6x2 – 8x = 0 Leading Coefficient → NEGATIVE → right arm down Degree → ODD → arms apart

Determine the end behavior: 4. -2x2 – 6x + 6 = 0 Leading Coefficient → NEGATIVE → right arm down Degree → EVEN → arms together