Now, let me give you an example of a function that is not surjective.

That is a function.

Floppy Drive

Flexible Grid

Flexible Pipe

So f is invertible.

Bracketing to HDR

So this is not a function.

So this is not a function!

Maria's billing function?

Uh...I'm flexible

So the unique solution to the equation f of x is equal to f of a is equal to a.

We have the cost function right here.

That's a pretty straightforward function.

This is a function.

Do the points on the graph below represent a function?

this is essentially like a two variable function.

And that's a function of a.

So this is not a function.

So this is an increasing function.

And this is going to be another function.

I'll have a general function.

She is flexible in her opinions.

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.

We could use any of the trig functions.

So this cannot be a function.

That's why it's called a linear function.

Such that f of x is equal to y.

Plus, what's the derivative of a constant function?

So what's the function for the combined area?

Or is there some other function?

And so when you transfer stuff via this pilus, or the plural is pili, this is called conjugation, bacterial conjugation.

This computer has a floppy disk drive.

They're very flexible, intelligent animals.

There were flexible, clear blood vessels.

I've learned to be flexible.

The wing motor is very resilient.

So this is our new f of x.

Or, you know, some function of epsilon.

So any function has a unique inverse.

The equation f of x is equal to y.

So let's apply our f inverse function to this.

Let's call that f of a right there.

So this was our combined area function.

Maybe I have a function let me make it like this.