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Basic Polynomial Graphs - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Graphing a basic cubic polynomial, so in this problem we are looking at f(x) is equals to x ³ cubic function no nothing else going on. So we are going to make a table figure out some points and then plot those to get the rough idea of what this graph is going to look like.

So if x is -2 we plug -2 in, -2 to the third is we have three negatives so those stay negatives this turns into a -8. Plug in -1, -1 to the third 3 negatives so it stays negative, -1, 0 to a third 0, 1 to a third is 1 and 2 to a third is 8.

No we have a set of points let’s plot this graph to see what it looks like. Again I’m not concerned with being exactly precise so we are just going to figure a rough sketch of what this looks like, I don’t even think I went up or down 8 it doesn’t really matter.

Okay so the point (-2,-8) go over 2 and then down 8 so that’s going to be down here always. (-1,-1) right, here (0,0) (1,1) and lastly (2,8) we get over 2 and up a bit and may not be on our chart, doesn’t really matter just trying to get the general look and then connect the dots. So we come down look like this, okay.

So what we actually have is the beginning sort of looks like a parabola what we did over with our x² term but the second half gets flips upside down, so this is the basic graph for any cubic function. Found our points in our graph.

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