Polynomial Functions Chapter 7, Sections 1 and 2

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

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

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)

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.

Describe the Graphs:

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:

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.