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# Equations vs. functions

CCSS.Math:

## Video transcript

I'm here with Jesse row of Summit prep you teach what classes you teach I teach algebra geometry and algebra 2 and now you're with us luckily for the summer doing a whole bunch of stuff as a teaching fellow yeah as a teaching fellow I've been helping with organizing and developing new content mostly on the exercise side side of the site and the reason why we're doing this right now is you had some very interesting ideas or questions yeah so as an algebra teacher when I introduced that concept of algebra to students I get a lot of questions one of those questions is what's the difference between an equation and a function the difference between an equation versus a function let's that's it's an interesting question let's pause it and see let's look the let the viewers try to think about it a little bit and then and then maybe we'll give a stab at it sounds great so Sal how would you answer this question what's the difference between an equation and a function let me let me think about it a little bit so let me think I think there's there's probably equations that are that are not functions and functions that are not equations and they're probably things that are both so let me think of it that way so let's first think of so I'm going to draw if this is the world of equations right over here this is the world of equations so this is equations equations and then over here is the world of functions that's the world of functions I do think there is some overlap we'll think it through what what where the overlap is the world of functions so an equation that is not a function that's sitting out here I think you know a simple one would be something like is something that like X plus 3 is equal to 10 I'm not explicitly kind of talking about inputs and outputs or relationship between variables I'm just dating an equivalence the expression X plus 3 is equal to 10 so this I think traditionally would just be an equation would not be a function functions functions essentially talk about relationships between variables you get one or more input variables and it will give you only one output variable I'll output value and so you could have something like and you can define a function and we'll do that in a second you could define a function as an equation but you can define a function a whole bunch of ways you can visually define a function maybe is a Graff so something like this where maybe I actually mark off the values so it's one two three those are the potential X values and and then on the vertical axis I show what the value of my function is going to be literally my function of X maybe that is one two three and maybe this function is defined for all non-negative values so this is zero of X and so let me just draw so this right over here at least for what I've drawn so far defines that function I didn't even have to use an equal sign if X is 2 if X is 2 at least the way I drew it Y is equal to 3 you give me that input I gave you the value of only one output so that would be a legitimate function definition another function definition would be very similar to what you do in a computer program something like you know if you input you input the day so let's say that you input the day of the week you input the day of the week and if day is equal to Monday Monday maybe you output output cereal so that's what we're going to we're going to eat that day and otherwise otherwise you output otherwise you output meatloaf so this would also would also be a function where we only have one output for any one day of the week we're only saying we can only tell you cereal or meatloaf or not there's no days where you are eating both cereal and meatloaf which sounds kind of kind of repulsive and and then if I were to think about if I were to think about something that could be an equation or a function I guess the way I think about is an equation is something that can be used to define a function so for example we could say that Y y is equal to 4x minus 10 this is a potential definition for defining Y as a function of X you give me any value of X then I can find the corresponding value of y so this is this is at least how how I would think about it