Chapter 3.4, Problem 62E

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

$P\left(x\right)=3x^5-5x^3+2xQ\left(x\right)=3x^5$

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

(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.