1. Polynomial Functions
Chapter 7, Sections 1 and 2

2. What is a Polynomial Function?
Equation:
Degree of a polynomial – the highest exponent
This is also the number of solutions
Examples:

3. Types of Polynomials Name Equation Deg Graph # Sol Constant Linear
Quadratic
Cubic
Quartic
Quintic

4. Evaluating Polynomials
This means to find the value of the function at a given x value
Substitute the x value into the function
Examples:
f(3)
g(-1)
f(2)-g(1)
g(0)+f(2)
f(a)
g(h-2)

5. End Behavior of Polynomial Functions
If f(x) has an odd degree, then f(x) is an odd function
The end behavior of odd functions goes in different directions
If f(x) has an even degree, then f(x) is an even function
The end behavior of even functions goes in the same direction
Recall: the number of real zeros is the number of times the graph crosses the x-axis
To describe the end behavior, look at what the y values are doing as x gets larger and as x gets smaller.

6. Describe the Graphs:

7. Max and Min of Polynomial Functions
Relative max – the highest peak in the graph
Relative min – the lowest peak in the graph
These are called relative because the graph increases or decreases in another place
These work the same as they did with quadratic functions
Examples:

8. Classwork Homework: Exit Slip Page 43 in workbook Page 44 in workbook
Problems 5-19
Page 44 in workbook
Problems 1-4, just find any of the relative max and/or relative min
Exit Slip
Compare/contrast a quadratic function with that of a general polynomial function.