Activity 1: The Leading Coefficient Test
ACTIVITY1: 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. identify the leading coefficient as positive or negative, and the degree of the polynomial as odd or even.
b. determine the end behaviors of the graph of a polynomial functions as x increases or decreases without bound.
Activity
1. Move the sliders n and a and observe what happens.
2. Observe the end behaviors of the graph on both sides 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)
Question 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?