Graph of Cubic Function - College Algebra

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We just talked about the parent function for a cubic functions, f of x equals
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x-cubed. So I thought I should show you the graph of this function. Here it is,
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this blue, pretty curve. You can see that this has the same overall behavior, as
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the other cubic function that we saw in the last example. That one looked a
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little more like this. You can see that the overall behavior is the same. One
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end of the graph is going down to negative infinity, and the other end of the
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graph is going up to positive infinity. In the middle, there's sort of a grey
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area of, in this case, going down and then going up again, and in this case,
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sort of leveling out for a bit. Now as I said in the last quiz, this parent
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function looks really different from the parent function for quadratic
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functions. Let's just add that on to our graph, so we can compare them more
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easily. So here, once again, is the parent function for a quadratic function, f
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of x equals x squared. Let's examine the overall behavior of this graph as well.
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We know that the general shape of a parabola is kind of like a u, or if it's
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upside down, like an n. Whether it's opening upward or opening downward, the
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parabola has a vertex, which is either its minimum or its maximum. And then both
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of its ends point in the same direction. And then as x gets further away in
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either the negative direction,or the positive direction, the graph points the
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same way. Either both ends of it go to positive infinity, or both ends go to
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negative infinity. We also talked earlier about how a parabola has an axis of
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symmetry running down the middle of it. So that if you fold the graph in half
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along that line, it will exactly map to the other side of itself. That's not the
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case over here with x cubed. If we simply fold this graph in half, down the
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y-axis, this right side is not going to end up looking just like the left side.
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It'll look more like this, not the same. This is all really interesting stuff.
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Now since we're increasing powers, why don't we just do that one more time. So
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I've put both y equals x squared and y equals x cubed on the same coordinate
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plane, then I draw another graph over here for you. My question for you now is
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what function does this graph represent? Now think about what this graph does on
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either side of the y axis. And also think about what points you'd expect each of
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these functions to go through. Your choices are y equals x, y equals x squared,
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y equals x cubed, y equals x to the fourth and y equals x to the fifth. So you
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can always make a t chart and plug in some points and see which of those t
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charts best matches this graph.
タイトル：
Graph of Cubic Function - College Algebra
Video Language:
English
Team:
Udacity
プロジェクト：
MA008 - College Algebra
Duration:
02:36
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