# Function Notation - Concept

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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