End Behavior of Polynomials
Investigation
Activity 1
1. Plot the polynomials_ 
__ and 
_ on the same grid on your graphing calculator._ Use the viewing window [-8, 8]_ by [-15, 15]._ Describe the differences in the two graphs. Describe any similarities as well.
2. Go to TABLE SETUP._ Let TblStart = 0 and ΔTbl=1 ;_ Indpnt: Auto; Depend: Auto._ Press 2nd GRAPH.
_____ Compare the values of Y1 and Y2 when x is close to 0, say between -5 and 3._
3.__ Now set your viewing window to [-50, 50] by [-5000, 5000] and press GRAPH._ _ What do you _____________ notice
____ about the two graphs now?__
4._ In the TABLE SETUP menu,__ let TblStart = 0 and ΔTbl=200._ Now press 2nd GRAPH and compare the _____________ values of Y1 and Y2 ._ What do you notice when the values of x get very large in either the _____________ positive or negative direction?
__ __ 5._ In Y3=, type in_ 
(the last three terms of the original polynomial)._ Go to the table and _____________ note how the values in Y2 compare to the values in Y3 when x is close to 0….then when x is huge in _____________ either the negative or positive direction. What do these values tell us about the leading term?
Activity 2
REPEAT THE ABOVE INVESTIGATION WITH THE POLYNOMIALS_ 
__ and 
Activity 3
REPEAT AGAIN WITH THE POLYNOMIALS 
and 
Activity 4
Now choose obnoxiously huge coefficients for the quadratic term and the linear term in a cubic polynomial._ Try for example 
._ Do you think that when the values of x get large enough, the first term will over ride all the other terms?_ Experiment a bit and discuss; your findings with a partner.