100, you end up with about five thousand features.

Our equation from before, 2n 2 n just becomes Θ(n).

This is equal to plus or minus b over a x.

If f(n) is in little o(g(n)), that's kind of like saying f(n) is strictly less than g(n).

And here, it's going to keep getting closer and closer to the asymptote on that side and then on that side.

And you notice that the sigmoid function, well, it asymptotes at one, and asymptotes at zero as

That's not the exact word, but it would look something like that where it's below the asymptote here.

But I think you get it at this point.

So a hyperbola, if that's the x, that's the y axis, it has two asymptotes.

It's going to come down and then go off, and never quite touch the asymptote, but approach it.

It just gets closer and closer and closer, arbitrarily close to the asymptote.

When you're taking the positive square root, we're always going to be slightly below the asymptote.

Asymptotes of a Hyperbola

So x is equal to 1 y is equal to minus 1.

So that's one asymptote.

So we're always going to be a little bit above the asymptote.

Hyperbola by Asymptotes Point

Because it will never, a hyperbola will never cross the asymptotes.

Okay, lets move on the, the third and final guiding principle.

The two asymptotes of a hyperbola.

Oh woops, not using my line tool.

Let's draw our asymptotes.

Go out there.

I know you can't read that.

Which essentially b over a x, plus or minus b over a x.

So that tells us that were always going to be slightly below the asymptote on the positive square root, and we're always going to be slightly above the asymptote on the negative square root.

The positive square root is the top line.

So that line would look like that.

Good enough.

Got to have a steady hand.

And then go like that.

So it'll go 3.

So it's going to get really close to the asymptote, and then go off, and go off in that direction.

The asymptote is this thing, but we're always going to be slightly below it.

Let's do that.

So if these are the axes, then if I were to draw let me draw some asymptotes.

So it's approximately linear around F of X equals zero, but it levels off to zero and one as we go to the extremes.

Construct a conic with this asymptote

Construct the asymptotes of this conic

Square root of 4 over square root of 9, times x.

And since you know you're there, you know it's going to be like this and approach this asymptote.

Let's say it's this one.

It's going to get closer and closer, and then here it's going to get closer and closer in that direction.

And this would've been the two lines of the asymptotes if we were centered at 0.

In other words, from an asymptotic standpoint, in this algorithm, we'll run the same worse case asymptotically then check both of the boxes.