College Algebra 3.2

3.2 Polynomial Functions of Higher Degree ,[object Object],[object Object],[object Object],[object Object],[object Object]

A. “Power Functions” look like x n ,[object Object],[object Object],[object Object],[object Object],[object Object]

B. Max number of Turning Points: ,[object Object],[object Object],[object Object],[object Object]

What do I mean by SHOOP? ,[object Object],[object Object]

[object Object],[object Object],[object Object]

If degree is n, then the maximum # of turning points is n-1. ,[object Object],[object Object]

C. Leading Coefficient Test ,[object Object],[object Object],[object Object],[object Object]

END BEHAVIOR! (What is the graph doing at extreme left and extreme right?) The l.c. gives us info about the right side, and then we can figure out the left side with a little thinking.

[object Object],[object Object]

Let’s consider f(x) = -x 3 +4x ,[object Object],[object Object],[object Object],[object Object]

Consider f(x) = x 4 -5x 2 +4 ,[object Object],[object Object],[object Object]

Describe right and left handed behavior:

D. Zeros and Multiples ,[object Object],[object Object]

If “a” is a zero, then also (a,0) is a point on the graph, and also, (x-a) is a factor. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Now we are going to use all those techniques to graph a function: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

f(x) = 3x 4 – 4x 3 ,[object Object],[object Object],[object Object],[object Object],[object Object]

College Algebra 3.2

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College Algebra 3.2