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# Recognizing functions from table

CCSS Math: 8.F.A.1, HSF.IF.A.1

## 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.