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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
Riley, do you remember when we first starting graphing functions? Like
with a ‘‘T-chart?’’
I remember everything.
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?’’
Then we learned about the slope-intercept form of a line. Good-old
Yeah, but lines are really boring. What about polynomials? What could
you tell me about just by looking at the equation?
Hmmmm. I’m not sure…
When is a large number (furthest from zero), which term of is largest (furthest
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?
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.’’