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When I'm studying for my test, I'll just make sure I go back up on YouTube and watch the video so I can listen and see exactly how I get to this topic.
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Because so far, we've worked on, here's my x and my y. We can also, let's do actually this one, f of x.
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Because I need you guys to understand, these are interchangeable, f of x and y are interchangeable.
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With sense we're talking about functions, Chris, we're going to be using f of x more commonly.
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In previous videos, not for you guys yet, but I'll have them up. For previous videos, we've talked about how to find what we're trying to do is to try and find how those x and f of x relate to each other.
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How does x and y relate to each other?
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What we're doing is, remember, we're looking at functions, we're saying what is happening to my x variable to get to either my f of x or my y.
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Remember, we talked about relationships, remember we had that talk, relationships, how are they related? What is happening to one to get the other?
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That's the whole, under thing, we're talking about relations.
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So, the first thing I always do is, I kind of like to look at the steps.
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The first thing I do is, hey, let's look at add and subtracting. That's the easiest one to make.
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So, I stay from 3 to 7, if I add a 4 to my 3, I get 7, right? So, therefore, you can say, hey, that makes sense.
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Let's write my function as f of x equals x plus 7.
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But remember, x represents all the numbers, not just this one. So, even though x plus 4, sorry, even though x plus 4 works for this, it has to work for every single one.
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So, if I put in a different x, does it still work? If I put in 2, does 2 plus 4 give me 5? No.
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So, therefore, this rule, does it work? Okay? No, I'm not function. Well, it's not a no-switch-not function, because remember, functions are determining if they have a unique x every y.
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And these are all functions, because every number relates to a number up there. But that's a different video, a different topic, doesn't it?
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So, let's look at, so adding subtracting does work. Let's look at multiplication. Here, I can't multiply by number. Here, if I multiply negative 1 times 1, I get negative 1, right?
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So, I could say my function can be f of x equals x. Whatever I put in for x, that's what I get for f of x, right?
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Was that true for us, if I put in 3, do I get back out through? No. So, remember, even though it works for this one, it has to work for all of them. So, therefore, this one doesn't work.
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Okay? So, now what we need to do is we need to look at combinations.
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And what we're going to do is we're going to look at multiplying, dividing, and and subtracting. So, the first thing I like to always try to do is always look at adding and subtracting first, and then doing a multiplication problem.
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So, when we're looking at a problem like this, I could say, alright, well, since it goes from positive to positive, and a negative to a negative, if I'm going to be multiplied by a number, that number has to be positive, right?
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Because if I'm not multiplied by a negative number, it would make that seven negative, right? And if I'm multiplied by a negative number against negative one, that would make that positive. So, I know I'm multiplied by a positive number.
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So, therefore, we're just going to have to kind of use options, right? So, what can I multiply three by to get me close to seven? Yes. You can multiply by two. What else could you do?
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Multiply by three, right? You can multiply by four. So, let's just practice. Let's just look at, let's just look at, let's just do two, three, and four. So, I can do f of x equals two x, f of x equals three x, and f of x equals four x.
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Okay? So, if I did two times x, that means two times three, that gives me six, right? To get to seven, I have to do what? Add one. So, that's one possible function. If I do times three, three times three is nine, to get to seven, I have to do one.
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minus two. And if I did four, three times four is twelve, to get to seven, I have to subtract five. Now, there's more possibilities. I'm just kind of doing the easiest ones right now.
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All right? Well, you guys, you'll see there could be, you know, there's multiple different ones. You can multiply by five. You can multiply by, you know, thirty, whatever. There's a lot of different possibilities. So, now, remember, x is for all of these values. It doesn't just work for this one. So, now, which one of these equations works for this one?
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Well, two times three is six, and six minus two. When I choose four, almost. So, we're almost there, almost there. But, yes, if you have the first one, multiply by two, add one.
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Does it work for this one? Negative two times two is negative two, plus one is negative one. So, therefore, my function is that that equals two x plus one. Does it make sense?
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So, you just got to, you got to get used to these guys. You're not going to get good at it unless you're practicing over and over and over on do these.
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So, this one is a very simple one again. Again, we look at it here. It have to add seven, right? So, I can say f of x equals x plus seven. However, negative two plus seven is a positive five, not a negative five, right? So, this doesn't work.
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What about multiplication? There's no positive number or integer. I'm sorry. There's no integer that I can multiply eight by the get to fifteen.
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No, for the rest of these. So, therefore, there's no multiplication I can do. Or division. Well, number, this is number six.
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And then, so, I'm going to have to do a combination again. So, let's just practice. What? There are some numbers I can multiply eight by the get to fifteen.
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Come off by by two, right? And let's do three. I don't want to get too far away, but let's just do f of x equals two.
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Two x and f of x equals three x. So, when I'm doing f of x equals two x, f of x, three x. Two times eight is sixteen.
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Minus one is...
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So, that works. And then, this one, if I did twenty four, so it'd have to be twenty four minus nine, right?
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Okay, so which one works for this one? Let's do two times negative four is a negative eight. Minus one is negative nine.
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And this one is three x minus nine. So, that works for this one, but does three times negative four is a negative twelve. Minus nine is a negative twenty one.
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So, it doesn't work for this one, right? So, this function is...
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Right there.
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Can I see it? Good? Good?
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That's it. What I got to do.