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.[br][br][b]Objectives[br][br]At the end of this activity, you will be able to:[br][/b][br] a. identify the leading coefficient as positive or negative, and the degree of the polynomial as odd or even.[br] b. determine the end behaviors of the graph of a polynomial functions as x increases or decreases without bound.

[b]Activity[/b][b][math][/math][/b][br][br]1. Move the sliders [i]n[/i] and [i]a and observe what happens.[br][/i]2. Observe the end behaviors of the graph on both sides if:[br] 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?[br] 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?[br] 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?[br] d. the degree of the polynomial is even and the leading coefficient is negative? Is it rising or falling to the[br]left or to the right?[br][br](This activity illustrates the leading coefficient test)[br][br][b]Question for Discussion[br][br][/b]1. Given the following functions, how would you describe the end behaviors of each graph using the leading coefficient test?[br] a. [math]f\left(x\right)=3x^4+2x^3-x^2+1[/math][br] b. [math]g\left(x\right)=-3x^8-5x^5+3x^2-5[/math][br] c. [math]h\left(x\right)=3x^{13}+5x^8-3[/math][br] d. [math]p\left(x\right)=-5x^{11}-2x^7+x^3+5[/math][br]2. How do the degree of the polynomial and the leading coefficient affect the end behaviors of the graph of a polynomial function?