 In this video I'm going to talk about determining whether a relation is a function. So basically what we're going to do here is we're going to look at a couple of actually real life examples of when something is a relation, hopefully getting a better understanding of what a function is. Excuse me. Try to determine whether a relation is a function. Because there's many, many things that have relationships. There's two different items that will have relationships. But does that relation actually, is that relation actually a function? That's what we're trying to determine here. Get a better understanding of what a function actually is. Okay, so a little bit of vocabulary here before we get started. A function, I like to think of it this way. A function for every input, you have a unique output. So for every time you plug something in, you're only going to get one result. That's kind of how I see a function. Okay, there's lots of different ways to look at it. But that's kind of my way of, my simple way of understanding what a function is. For every input that you have, you're going to have a unique output. So whenever you plug something in, you're only going to get one answer. You're only going to get one solution or you're only going to get one thing. So we're going to use a couple of real life examples to try to get a better understanding of what a function is. Okay, so determine whether each relation is a function. So here we go. These are two separate relations. You've got one on the left here, one on the right. I'll start with the one here on the left. And the items in a store to their prices on a certain date. Okay, so the items in a store to their prices on a certain date. Okay, so we have items in a store. Let's actually just start with that. Items in a store. So I go to the grocery store with mom and dad because I'm a good son or daughter. And I go grocery shopping. I'm picking up a couple of things. We get Doritos. We get cereal. We get a couple of things. So a couple of things that you can get at the store. We can get chips, Doritos, whatever it is that you like. You can get chips. We can get cereal. We can get milk. And we can get, I don't know, lunch meat. Yeah, lunch meat for sandwiches, something like that. Okay, just a couple of things you can see in the store. Now the thing is, is writing these down, these are kind of the first, these are the, this is the first piece of my relation. Again, relations is a comparison of two different things. So here's my first set of things. These are all just things in the store. Okay, so two, now this two where that's kind of want to pay attention to. This kind of gives you the division between your two things. The items in the store, two, their prices on a certain date. So that's kind of the division between the two. How you can tell what my two, what my two pieces are, what my two pieces in the relation are. Okay, so items in the store, here's four items that we have. And then their prices on a certain date. Now we actually have to say certain date, because some items will go on sale one day, so it'll be different prices other days, something to that effect. But I get chips maybe two for $6 one day, and then the next day they're $4.50, back up to the regular price, whatever the case may be. So we're putting here on a certain date, so we're just looking at one day, we're not looking over the course of a week, or something to that effect to really confuse us. Okay, so we're looking at the prices for on a certain date. So chips, chips on this certain date are usually going to be something to the effect of about $4.50, something like that. Okay, sometimes you're Doritos, sometimes you're Lace, chips, whatever they are, they're about that. Okay, cereal, cereal on the other hand is going to be just a little bit cheaper, maybe I'm buying, maybe an Off-Brand or something like that, we're going to go with $2.89 for a box. Okay, now for milk on this certain day, maybe milk is on sale, and then milk is also going to be $2.89. Okay, stocking up on milk for the week might buy a couple of gallons, something to that effect. Now, notice here that I've got two arrows going to the same price. This is going to be okay, we'll talk about this here in a minute. Okay, lunch meat on the other hand, this is going to be, let's get a round number of about $5. So $5 for a pound of sliced lunch meat for lunches for school or whatever the case is. Okay, so now as I look at all these numbers, this is just a random example to come up with nothing too extraordinary. But I have chips, cereal, milk, and lunch meat. These are all my inputs. This is all the first part of my relation, from the items in the store. These are my inputs. So these are things that I put into my cart. And then these are the prices, these are the outputs. These are the prices on that certain date. Okay, now the thing is, we want to figure out, is this a function or not? Okay, so again, a function is, for every input, there is a unique output. So whenever you plug something in, you're only going to get one answer. Okay, you're only going to get one answer. So, okay, so if I plug in chips, if I put chips into my cart, they're only going to be $4.50. Now we're speaking of specific type chips. We'll go Doritos. So when I put Doritos in my cart, they're only going to be $4.50. Because if that's what they say on the shelf, when it goes up to the counter, that's what they're going to ring up at. It's not going to change. That's what we call a unique output. So a single input of my Doritos gets a single output of $4.50 up at the register. Okay, same thing here. Serial is $2.89 for this box of cereal. Okay, so again, when I get cereal, it's not going to be a different price. It's going to be the same price I see on the shelf. $2.89. Now this work might get a little confusing, but again, you just stick with the same logic. Milk is then when I look at milk on the shelf, it's $2.89. So milk, when I go up to the register, it's still going to be $2.89. That's a unique price for milk. Now yes, cereal and milk do share the same price, but what we're looking at is a function for every input. It has a unique output. A function, whatever you plug in, I'm only going to get one result. So when I put milk into my cart, it's only going to be $2.89. That's okay. Yes, you can have multiple items that go to the same price, but it's still going to be okay for a function. Okay, and then luncheon meat on the other hand, same thing with chips up here. Lunch meat has a unique answer of $5. $5 for a pound of lunch meat. Okay, so this case, this one is actually a function. This is an example of a function. Okay, so this is an example of a function. And again, this right here, it might be a little bit confusing since they're going to the same number, but again, you've got to remember, functions for every input, there's a unique output. So for whenever I plug something in, I only get one answer. When I plug cereal in, I get one answer. When I plug milk in, I get one answer. That's okay for a function, even though you get to the same answer of $2.89. Okay, so that's one example. That's one example for a function. We're going to look at this other example, let me change colors a little bit. So from the types of fruits to their colors. Okay, so from the types of fruit, and again, it's a relation relating to things, so the types of fruits, two, I think in that two word there, it's going to divide us between our two different things relating. So fruits to their color. So a couple of fruit that I could have, I could have apples, I could have pears, I could have strawberries, straw, oh, there's supposed to be an R in there, strawberries. That's enough, I think. About three different examples of different types of fruit. Okay, now here's the thing though, is that apples, if you go to the store, apples, they can be red, they can be yellow, and they can also be green. This causes a little bit of a problem. Apples can be red, they can be also yellow, they can also be green. Okay, now this is actually a very, very bad thing. Usually pears are usually going to be yellow, and strawberries are usually going to be red. So we'll go up here with them. Okay, now this right here, that's what causes our problem. Again, for a function for every input, there is a unique output. So whenever I put apples in, for it to be a function, it only should be one result. But in this case, apples, the relation of the fruit to their color, apples can be red, or they can be yellow, or they can be green. Apples can be all sorts of different colors. You can make the argument for pears also, pears can be yellow, and maybe a little bit green depending, depending on where their ripeness is. Strawberries, on the other hand, I guess when they're maturing, they're white and a little bit green, and then once they fully mature into a full fruit, then they turn red. But anyway, you get the idea that apples, they can be a bunch of different colors. Apples can be red, apples can be yellow, apples can be green, there's no set result, there's no set answer on what colors the apple is going to be. Okay, so this is an example of something that is not a function, not a function. Okay, not a function. And I know these are a couple of examples that don't really deal with numbers, but again, you can kind of see the similarity with numbers, especially with the example that we did over here, with the stuff that you see at the grocery store, and then the numbers of the prices on a certain date. So you can kind of see the connection with numbers there. Okay, that is determining whether a relation is a function, a couple of real-life examples of real-life relations, relations in real-life or actual functions. And again, as a reminder, a function, just got to remember, for every input there is a unique output. I also like to say it as functions, whenever you plug something in, you only get one answer. Whenever you, again, whenever you buy the chips on this certain date, they are only going to be $4.50. That is a function. On the other hand, apples, they can be red, they can be yellow, they can be green. There's lots of different colors for your apples. That makes it not a function. Those are the differences between the two. That is determining whether a relation is a function. I hope this video was helpful to you.