2. 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.

3. 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.

4. 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.

5. 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)

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

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

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

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