How crazy could it be?

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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 $y = mx +b.$
Devyn: Yeah, but lines are really boring. What about polynomials? What could you tell me about $y= 5x^6-5x^5-5x^4+5x^3+x^2 -1$ just by looking at the equation?
Riley: Hmmmm. I’m not sure…

When $x$ is a large number (furthest from zero), which term of $5x^6-5x^5-5x^4+5x^3+x^2 -1$ is largest (furthest from zero)?

$-1$ $x^2$ $5x^3$ $-5x^4$ $-5x^5$ $5x^6$

When $x$ is a small number (near zero), which term of $5x^6-5x^5-5x^4+5x^3+x^2 -1$ is largest (furthest from zero)?

$-1$ $x^2$ $5x^3$ $-5x^4$ $-5x^5$ $5x^6$

Very roughly speaking, what does the graph of $y=5x^6-5x^5-5x^4+5x^3+x^2 -1$ look like?

The graph starts in the lower left and ends in the upper right of the plane. The graph starts in the lower right and ends in the upper left of the plane. The graph looks something like the letter ‘‘U.’’ The graph looks something like an upside down letter ‘‘U.’’