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CCSS.Math: ,

we're asked to look at the table below from the information given is there a functional relationship is there a functional relationship between each person and his or her height so a good place to start just think about what a functional relationship means now there's definitely a relationship they say hey if you're Joel you're 5/6 if you're Nathan you're 411 if you're Stuart you're 511 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 so if you say height is the function height is a 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 if what is the height of Nathan what is the height of Nathan well you look at the table and say well Nathan's height is 4 foot 11 Nathan 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 and we can even see that on a graph let's let me graph that out for you so let's graph out so let's see the highest height here is 6 foot 1 so if we start off with well we don't have to start willis to me just start at one foot two feet three feet 4 feet 5 feet 5 feet and 6 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 Joel we have Nathan we have Stuart we have LJ and then we have thorak right there so let's plot them so you have Joel Joel height is five six so five six is right about there then you have Nathan Nathan tight let me do it in a different color Nathan's height is 411 so Nathan's height is 411 we will plot him right over there then you have Stewart Stewart ight is 511 so Stewart ight is 511 he is pretty close to 6 feet so Stewart's height I made them like 6 feet let me make a little Lord is 511 then you have LJ LJ height is 5/6 so you have two people with a height of five six but that's okay as long as for each person you only have one height and then finally tharok is six foot one he's the tallest guy here thorak is right up here at six foot one 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 okay 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 Stuart Stuart is is five foot is five foot three inches if this was our table then Nolen we would no longer have a functional relationship because for the input of steward we would have two different values if we were to graph this we have steward here at 511 and then all of a sudden we would also have Stuart at five three now this doesn't make a lot of sense so we would plot it right over here so for Stuart you would have two values and so this wouldn't be a value of a valid functional relationship because you wouldn't know what value to give if you were to take the height of if you were to take the height of Stuart you in order for this to be a function there can only be one value for this you don't know in this situation if I 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 Stuart 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 would not be a function