This is Turbo the Penguin.

So this is Turbo.

He met us and got his name because he started standing under my diesel truck a turbo truck, so we named him Turbo.

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

That is a function.

Oil, construction business, turbojet engines, PepsiCola....

So f is invertible.

Bracketing to HDR

So this is not a function.

So this is not a function!

Maria's billing function?

and you see, Turbo's pretty intent on his flipper patting.

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.

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.

Turbo has taken to knocking on the door with his beak, we let him in and he comes in here.

And you'll see soon that my graduate student ... and you see, Turbo's pretty intent on his flipper patting.

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.

That's what a lot of people said about turbo trading in financial exchanges 20 years ago.

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.

If you imagine our box, the function f.

So y is a function of x.