## ← Graph of Cubic Function - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

1. We just talked about the parent function for a cubic functions, f of x equals
2. x-cubed. So I thought I should show you the graph of this function. Here it is,
3. this blue, pretty curve. You can see that this has the same overall behavior, as
4. the other cubic function that we saw in the last example. That one looked a
5. little more like this. You can see that the overall behavior is the same. One
6. end of the graph is going down to negative infinity, and the other end of the
7. graph is going up to positive infinity. In the middle, there's sort of a grey
8. area of, in this case, going down and then going up again, and in this case,
9. sort of leveling out for a bit. Now as I said in the last quiz, this parent
10. function looks really different from the parent function for quadratic
11. functions. Let's just add that on to our graph, so we can compare them more
12. easily. So here, once again, is the parent function for a quadratic function, f
13. of x equals x squared. Let's examine the overall behavior of this graph as well.
14. We know that the general shape of a parabola is kind of like a u, or if it's
15. upside down, like an n. Whether it's opening upward or opening downward, the
16. parabola has a vertex, which is either its minimum or its maximum. And then both
17. of its ends point in the same direction. And then as x gets further away in
18. either the negative direction,or the positive direction, the graph points the
19. same way. Either both ends of it go to positive infinity, or both ends go to
20. negative infinity. We also talked earlier about how a parabola has an axis of
21. symmetry running down the middle of it. So that if you fold the graph in half
22. along that line, it will exactly map to the other side of itself. That's not the
23. case over here with x cubed. If we simply fold this graph in half, down the
24. y-axis, this right side is not going to end up looking just like the left side.
25. It'll look more like this, not the same. This is all really interesting stuff.
26. Now since we're increasing powers, why don't we just do that one more time. So
27. I've put both y equals x squared and y equals x cubed on the same coordinate
28. plane, then I draw another graph over here for you. My question for you now is
29. what function does this graph represent? Now think about what this graph does on
30. either side of the y axis. And also think about what points you'd expect each of
31. these functions to go through. Your choices are y equals x, y equals x squared,
32. y equals x cubed, y equals x to the fourth and y equals x to the fifth. So you
33. can always make a t chart and plug in some points and see which of those t
34. charts best matches this graph.