Functional Relationships 1 Functional Relationships 1
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- 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.
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