Chapter 2.6, Problem 66E

End Behavior of a Function By the end behavior of a function we mean the behavior of its values as $x\to \infty$ and as $x\to -\infty$

(a) Describe and compare the end behavior of the functions $P(x)=3x^5-5x^3+2xQ(x)=3x^5$

by graphing both functions in the viewing rectangles $[-2,2]$ by $[-2,2]$ and $[-10,10]$ by $[-10,000,10,000]$ .

(b) Two functions are said to have the same end behavior if their ratio approaches 1 as $x\to \infty$ . Show that $P$ and $Q$ have the same end behavior.