In this activity, you will explore different parts of functions which help determine the end behavior of a graph. You will interact with the given graphs, and look for similarities to come up with your conjecture which you will record in your notes.

With the applet below, explore the what happens to the graph as you change the degree of the polynomial function. Try to observe any patterns between the relationship of the degree and the graph. [br][br]

In the last example, we learned that our graph depends on if the degree of the function is even or odd. This is the first requirement to help us determine what we call the [b]"End Behavior"[/b] of a function, or how the function behaves as we look to the left and right sides of the x axis. [br][br]In the next Exploration, we will learn the second requirement to help us determine the end behavior of a graph of a polynomial function by looking at the Leading Coefficient of the Polynomial.

Use the applet below to observe what happens to the graph of an [b]EVEN [/b]degree polynomial as we change the value of the Leading Coefficient. [br][br]We will start by looking at the basic even degree function [math]y=x^2[/math].

Use the applet below to observe what happens to the graph of an [b]ODD [/b]degree polynomial as we change the value of the Leading Coefficient. [br][br]We will start by looking at the basic odd degree function [math]y=x^3[/math].