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## Algebra 1

### Course: Algebra 1 > Unit 8

Lesson 7: Recognizing functions- Recognizing functions from graph
- Does a vertical line represent a function?
- Recognize functions from graphs
- Recognizing functions from table
- Recognize functions from tables
- Recognizing functions from verbal description
- Recognizing functions from verbal description word problem

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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.

## Want to join the conversation?

- 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.

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:recognizing-functions/v/graphical-relations-and-functions

Hope that helped (even if it is after 3 years).(28 votes)

- Okay i have officially decided that i am stupid could sombody please explain it to me in a different way?

PLEASE!(8 votes)- 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.(22 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.(2 votes)

- 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)

- Just an idea... what if you had a three dimensional graph? One axis their names, one their height, and one their ages? That way you could have two people with the same name and it wouldn't be effected. As long as people with the same name have different ages. But the idea is, can you have multi dimensional functions / graphs? (this is the sort of thing that makes me like functions so much)(6 votes)
- The answer is yes! Multi dimensional graphs are a thing. For a 3-d graph to be a function, 2 inputs can only have one output. Let's say the third line is w. So you have 4(w)|5(x)|8(y). If you have another point as 4(w)|5(x)|9(y) it will not work. So if w is ages, x as names, and y as height. 10(w)|Celia(x)|5'3"(y) and 15(w)|Celia(x)|5'8"(y) will work! Even though it will be a little confusing graphing it, especially graphing it on paper, it will work as long as 2 inputs have only 1 output.

But I'll say, just stick with 2-d for now. Just add a last name to the name, or maybe just prime the name for a second x value, [insert name] and [insert name]'.

You can learn more in the multivariable calculus course on Khan Academy, as it introduces 3-d graphing. Hope that helps you with your questions! :3(5 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)

- 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!(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)

## Video transcript

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.