How Polynomial Degree Affects it's Graph

Objective

Students will examine multiple graphs, make conjectures from the graph's information and discover how the degree of a polynomial affects its domain, range, x-intercepts, turning points, and end behavior.

Lesson

• Students should already know how to find domain, range, x-intercepts, turning points (max's/min's) and end behavior of a given polynomial before beginning this activity
• Students need to be in groups of 3-4
• Give each group the set of polynomial graphs.  They fill out the information for each graph, cut them out and sort them by degree.
• Students will use the graphs to answer questions on the student worksheet.  They will then be asked to make conjectures about how the degree affects each aspect of the polynomial graph.
• When finished, given an equation students will describe the features of the graph (and/or sketch what the graph may look like).
• This activity should take about an hour

Materials Needed

Student Worksheet

Polynomial Graph Set

Virginia Standards of Learning

AII.6      The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.

AII.7      The student will investigate and analyze functions algebraically and graphically. Key concepts include:

               a)   domain and range, including limited and discontinuous domains and ranges;

               b)   zeros;

               c)   x- and y-intercepts;

               f)   end behavior;