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Recognizing functions from table
Checking whether a table of people and their heights can represent a function that assigns a height to a name. Created by Sal Khan and Monterey Institute for Technology and Education.
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- i don't understand how to tell whether a relation is a function or not.explain why or why not.maybe a video will help me.(17 votes)
- Hey! Don't worry. So basically you have a functional relationship if for your domain there is only one output. As simple as that.
Check out this video where Sal explains it better.
Hope that helped (even if it is after 3 years).(26 votes)
- Okay i have officially decided that i am stupid could sombody please explain it to me in a different way?
- Ok, so basically, he is using people and their heights to represent functions and relationships. 1 person has his/her height. He/her could be the same height as someone else, but could never be 2 heights as once. This goes for the x-y values. An x value can have the same y-value correspond to it as another x value, but can never equal 2 y-values at once. Hopefully, you understand this.(21 votes)
- i still dont get what a relationship in a funtion is(3 votes)
- A relationship is saying that an input is related to this output in some way.
Functions are relationships that have one y per x.(1 vote)
- So, a circle is not a function, correct?(6 votes)
- Yes, a circle is not a function. This is because it has 2 different y-values in the same x-position in some places. A easy way to see if something is a function is the vertical line test. You can imagine a vertical line going across the coordinate plane. If it ever intersects two points at once while it's going across, it's not a function. otherwise, it is.(13 votes)
- So just to clarify, you can have the same number in the domain, but not in the range?(5 votes)
- It's actually the other way around. Domain consists of the numbers you put into the function (x-values), and there can't be different values in the range (y-values) for the same x-value. There can be any amount of the same number for the range, no matter what the x-value is.(5 votes)
- Whoa whoa whoa, hold on...what if it's a different person with just the same name? What would happen then?(5 votes)
- You would either have to label by last initials, Nathan A. and Nathan K, or by numbers Nathan 1 and Nathan 2.(6 votes)
- Why does Sal place 5.11 higher than 5.6 on the graph?(3 votes)
- its not 5.11, it is 5 feet 11 inches. in that case, 5.11 has greater value on the graph.(5 votes)
- Does a linear function always HAVE to be a line, because on the Practice: Recognize Functions from graphs exercise it has problems that don't necessarily have lines and yet it still states that it is a linear function.(2 votes)
- Linear functions always create a line.
However, there are other types of equations and functions. I think the exercise is asking you to identify if the graph is a function, not necessarily a linear function.(6 votes)
- how do we solve something like y=3x+1 vs. y=(1/3)^x+1(4 votes)
- Are you talking about intercept form?(2 votes)
- What if there are 2 people with same name?(3 votes)
- if there are 2 people with the same name, then the table would no longer be a function! At3:29, Sal wrote Stewart: 5'3" to give us an example of what isn't a function!(3 votes)
We're asked to look at the table below. From the information given, is there a functional relationship between each person and his or her height? So a good place to start is just think about what a functional relationship means. Now, there's definitely a relationship. They say, hey, if you're Joelle, you're 5-6. If you're Nathan, you're 4-11. If you're Stewart, you're 5-11. That is a relationship. Now, in order for it to be a functional relationship, for every instance or every example of the independent variable, you can only have one example of the value of the function for it. So if you say if this is a height function, in order for this to be a functional relationship, no matter whose name you put inside of the height function, you need to only be able to get one value. If there were two values associated with one person's name, it would not be a functional relationship. So if I were to ask you what is the height of Nathan? Well, you'd look at the table and say, well, Nathan's height is 4 foot 11. There are not two heights for Nathan. There is only one height. And for any one of these people that we can input into the function, there's only one height associated with them, so it is a functional relationship. We can even see that on a graph. Let me graph that out for you. Let's see, the highest height here is 6 foot 1. So if we start off with one foot, two feet, three feet, four feet, five feet, and six feet. And then if I were to plot the different names, the different people that I could put into our height function, we have-- I'll just put the first letters of their names. We have Joelle, we have Nathan, we have Stewart, we have LJ, and then we have Tariq right there. So lets plot them. So you have Joelle, Joelle's height is 5-6, so 5-6 is right about there. Then you have Nathan. Let me do it in a different color. Nathan's height is 4-11. We will plot to him right over there. Then you have Stewart. Stewart's height is 5-11. He is pretty close to six feet. So Stewart's height-- I made him like six feet; let me make it a little lower-- is 5-11. Then you have LJ. LJ's height is 5-6. So you have two people with a height of 5-6, but that's OK, as long as for each person you only have one height. And then finally, Tariq is 6 foot 1. He's the tallest guy here. Tariq is right up here at 6 foot 1. So notice, for any one of the inputs into our function, we only have one value, so this is a functional relationship. Now, you might say OK, well, isn't everything a functional relationship? No! If I gave you the situation, if I also wrote here-- let's say the table was like this and I also wrote that Stewart is 5 foot 3 inches. If this was our table, then we would no longer have a functional relationship because for the input of Stewart, we would have two different values. If we were to graph this, we have Stewart here at 5-11, and then all of a sudden, we would also have Stewart at 5-3. Now, this doesn't make a lot of sense, so we would plot it right over here. So for Stewart, you would have two values, and so this wouldn't be a valid functional relationship because you wouldn't know what value to give if you were to take the height of Stewart. In order for this to be a function, there can only be one value for this. You don't know in this situation when I add this, whether it's 5-3 or 5-11. Now, this wasn't the case, so that isn't there and so we know that the height of Stewart is 5-11 and this is a functional relationship. I think to some level, it might be confusing, because it's such a simple idea. Each of these values can only have one height associated with it. That's what makes it a function. If you had more than one height associated with it, it would not be a function.