Two young mathematicians think about the plots of functions.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, do you remember when we first starting graphing functions? Like with a “T-chart?”
Riley
I remember everything.
Devyn
I used to get so excited to plot stuff! I would wonder: “What crazy curve would be drawn this time? What crazy picture will I see?”
Riley
Then we learned about the slope-intercept form of a line. Good-old
Devyn
Yeah, but lines are really boring. What about polynomials? What could you tell me about just by looking at the equation?
Riley
Hmmmm. I’m not sure…
When is a large number (furthest from zero), which term of is largest (furthest from zero)?
When is a small number (near zero), which term of is largest (furthest from zero)?
Very roughly speaking, what does the graph of look like?