WEBVTT
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Okay. A constant function is one of the first formulas. This is the lone easy one. What does
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it work constant mean? Always does the same. So constant function is always does say what?
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What do we use in math? So the function is always the same number. The function is always the same number. Here's an example. Here's one example.
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At the max equals 5. At the max equals 5. An example of constant function because what does the function always equal?
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Does it ever equal number other than 5 according to this? No. So it's constant. It's continually and forever equals 5.
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I think that's a question. Do you like guys that that forever? I'm going to get sharp. This starts going to confuse you for a bit. But you need to get used to this notation.
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Normally, I want to make a chart. I use x and y. I have x and I'm going to use element. Because there is no y. The function itself is like y.
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I don't want to say it is y. I don't want to have that direct correlation. But it is like we do it the same way. So x is one variable. And the function afflvax, that's what it's called, is another one.
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What's the function every single time? What? There we go. So this can make 5, 5. And x can be whatever most of you can get over.
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So I'm going to go over here. I'm going to make a graph. I'm going to plot those points. One, two, three, one, two, three, four, five, six, seven, one, two, three, four, five, three, five, seven, five.
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What do you think that is? What's that going to make? What kind of y? Orz on the x? That's right. And here's the zero.
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Afflvax, the function is like y. Why is the vertical? The function is vertical. If the vertical is one number all the time, it never goes down. Then you have a horizontal line. So the simplest way to say this is if you have a function equal another, it's what kind of line? And where is it?
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On the x side. How do you know where it is? Where's my hat? What number is this? What is that next equal? So how do you know where it is? What are the equals? Where is this one going to be? Say it loud.
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What is the answer? Graphome, all four go. I have to raise now.
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I'm going to show you how to graph all these. Again, they're going to look like a beat. They're going to look like a beat. Either going up or going down. Most of the ones in here, the side of them are going to be going up.
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Anyway, let me get started. The place where it sort of changes is called the vertex. What's it called? Vertex. Where comes to a point? Now, I want you to think about this. Where is the hinge point for absolute value to change?
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Zero. What happens when it's positive?
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It goes up. I'm talking about absolute value. What's your answer? It doesn't change, right? The same number. If you take the absolute value of a negative, it's the positive that same value, but it's changed.
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On one side of zero, you do nothing. On the other side of zero, what do you do? Let me write this up. I need you guys to look forward. I need you to look forward.
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So, if you guys are heads of down, you're drawn on your thing, and you're not going to learn jack squat that way. We have to find out who is. You did nothing. It's still three. You have to find a negative two.
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You do. You can't do opposite. Now, the reason why this looks like a V is because it's essentially two lines. Well, that's the positive. And one that's the negative.
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But it switches around this zero point, which we'll talk about. That's the vertex.
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I'm going to make two that's going to be the first two. So, what you're going to do, probably the simplest way for me to teach you is we're going to make a chart.
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On this chart, I'm going to have three points. Because I have a vertex, and then it goes out two ways. So, I need two points out here. So, I need the vertex, and then two things out here to get the graph.
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The way you find the vertex is where the absolute value, where is the turning point for absolute value? Zero. Where the absolute value is zero, that's the turning point, that's the vertex. So, look at here. Here's the absolute value.
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What makes that zero? Zero. Zero. Okay. What makes this is the absolute value? Only looking at the absolute value. What makes that zero? What makes it zero? What makes that one? What does it one?
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Zero. What makes it zero? Zero. Zero. I said only look at what? The absolute value. What makes that zero? Zero. What makes that absolute value zero? Zero. What makes it zero? What does it make it zero?
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The vertex is where the absolute value part, only that part, equals zero. So, in this case, in fact, in these first four cases, it's just zero. Because those, you know, we put in zero for x. Zero. But down here, it's x plus two, x need to be negative two to make it zero.
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Okay. So, I'm going to do the first two. This is how you start. You find out what makes the absolute value zero. In this case, it was zero. That's your x-coordinate of the vertex.
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Okay. So, the first point you're going to find is your vertex. The next thing you're going to do, if you have x, you can find the function. If I know x is zero, I'll have to find out the vertex.
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Well, you can. Well, you can. Well, you can. Well, you can. What do you get? Zero. Alright. Zero. You're going to start by graphing my vertex. Here's my vertex. Zero, zero.
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Then I need a point to the left side and a point to the right side. Because I have my center, my vertex, I need something to go to the left and something to go to the right.
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Or it can go to the left down this way or it can go to the right down this way. So, here's my point. What's to the left? Negative number. Well, pick one. Negative number.
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Wow, that's really far. Negative one. Negative one. There you go. There you go. I don't like that.
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So, if x is negative one and I plug it in, what's the absolute value of negative one? One. One. So, now I have a point that's to the left. Negative one. One.
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See that is about right? There. Okay.
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Now, pick a number to the right. One. Okay. Pick a lot again. Well, I guess, sort of the same. Two. If I plug in one, let's see, I have some value of one. One. One.
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That's to the right. One, one. And now, which one's my vertex? Zero. So, this is my vertex. That's where everything comes out.
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Everything starts there and comes out. So, I draw my graph starting there and going out through those other two points.
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Like that. There's the graph.