Copy of Activity 1: The Leading Coefficient Test
THE LEADING COEFFICIENT TEST (Determining the End Behaviors of the Graph of a Polynomial Function)
In this activity, we are going to investigate the effects of the leading coefficient and the degree of the polynomial function to the end behaviors of its graph as x increases or decreases without bound.
Objectives
At the end of this activity, you will be able to:
a. state the relationship of the leading coefficient and the degree of the polynomial.
b. determine the end behaviors of the graph of a polynomial functions as x increases or decreases without bound.
Activity
Move the sliders n and a, and observe the end behaviors of the graph as x increases or decreases without bound if:
a. the degree of the polynomial is odd and the leading coefficient is positive? Is it rising or falling to the left or to the right?
b. the degree of the polynomial is odd and the leading coefficient is negative? Is it rising or falling to the left or to the right?
c. the degree of the polynomial is even and the leading coefficient is positive? Is it rising or falling to the left or to the right?
d. the degree of the polynomial is even and the leading coefficient is negative? Is it rising or falling to the
left or to the right?
(This activity illustrates the leading coefficient test)
Questions for Discussion
1. Given the following functions, how would you describe the end behaviors of each graph using the leading coefficient test?
a.
b.
c.
d.
2. How do the degree of the polynomial and the leading coefficient affect the end behaviors of the graph of a polynomial function?