Throughout mathematics, we find function notation. Function notation is a way to write functions that is easy to read and understand. Functions have dependent and independent variables, and when we use function notation the independent variable is commonly x, and the dependent variable is F(x). In order to write a relation or equation using function notation, we first determine whether the relation is a function.
One thing you'll find in your math classes is that there's lots of different ways to write the same thing. And although sometimes it can be confusing, it's actually pretty cool, because it helps you keep track of what variable or what letter is affecting which one.
Like, for example, most of the time X is the independent variable. And Y is the dependent variable. What that means is that your Y value depends on whatever X was. X can usually change on its own. And whatever X does affects what Y is. That's why we call Y the dependent variable.
So one way this is written is it's kind of different from what you've seen before. What you've seen before is probably something like this. Y equals 3X plus 2. A new way to write that is using what's called function notation. Instead of Y, I'm going to say F of X. What that means is the function that's using X is equal to 3X plus 2. It's the same thing written in two different ways.
I think it's kind of neat when we get into doing some more problems with numbers is that I can stick a number in there for X and I can show what number that is here as well. You can kind of tell what X number you're plugging in, the independent variable, to get your Y value output variable.
One last thing to keep in mind when you're working with functions and function notation is the ideas of domain and range. Domain is the set of all X values or the independent variables. Range is the set of Y values or the dependent variables. Which means that your domain changes on its own. It's independent. Your range is dependent on that domain stuff.
It's a lot to keep track in your head. As you can tell my head is kind of struggling with it, too. But you can see as we get going with some problems you can keep it all straight and do a good job with notation function.
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