let me, this is x.

So let x equal the number.

Let me get rid of my little let x statement.

Let me just not take an x.

Then let me draw my x axis.

Actually let me draw x, x we could draw as 2, 3.

Let me, let me define a function as this f(x) is equal to x squared plus 1 if x is even and equals x squared minus 1 if x is odd.

Let me graph y equals x. y equals x. y equals x is that line right there.

So let x equal what I start with.

Let me draw my x axis right here.

So let set this equal to a variable, let me call this x.

Let me call this x . If we call the measure of that angle x

Let me draw my x axis, just like that, that is my x axis.

(X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Cast off everything (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Let your heart burn

(X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Cast off everything (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Let your heart burn

Let me to define let me say f of x is equal to x squared when, if x does not equal 2, and let's say it equals 3 when x equals 2.

Let me take the x out of that side.

Let me write this. x squared plus 4x over x plus 3 times x squared minus 9, all of that over x squared plus x minus 12.

So let me draw. x squared looks something like let me use a different color. x square looks something like this, right?

Let me draw the graph of f(x). f(x) is equal to x squared, or Y is equal to x squared, either one.

(Your heart will break within) (Your heart will break within) (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Cast off everything (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Let your heart burn (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Cast off everything (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Let your heart burn

If we substitute x squared in for y. x squared to the third power is x to the sixth. x to the sixth times x let me write that.

Let me think. three times x plus five is equal to eight times x plus two.

So let's let x, x is equal to the number that 150 is 25 of, right?

Well then I could say, let x be the price

So let's say that I have the function f(x) let me, just for the sake of variety, let me call it g(x).

So let me just define x diamond x diamond y and I'm going to define that as

So this would be let me switch to green we get x plus two, and since I'm using green, I'm just going to stay with green. x plus two, let me switch to orange. x plus two times x plus x plus two times three.

So let x be equal to the number of tiles purchased.

Let me do that. y is equal to minus x squared.

So we can write that x let me write that down.

Your heart will break within the quaking noise (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Cast off everything (X!!!) Try to feel it (X!!!) Try to shout out (X!!!) Let your heart burn

Let's have let me say, x plus two over x plus one is equal to, let's say, seven.

Suppose we let x go to infinity, then x Mu2 for any fixed Mu would go to infinity.

Let me do it. x plus a, squared, is equal to x squared plus 2ax plus a squared.

Let me define my new p of x, so let me add another term. p of x, the first terms are going to be the same.

Or actually, even better, let me do this a little bit. x squared plus 6x plus 5 over x squared minus x minus 2.

So let me just pick some arbitrary x values right here, and I'll stay in the positive x domain.

Let me write, this could be x and this would be 2x.

Let me just draw a quick and dirty x and y axis.

So let's see, let me draw some what is the x intercept?

Let me set the initial state to be x, y, and orientation.

If we said x (Let me do it in that same color.)

So let x be the highest marked price that I can afford.

Let me write that. x plus x plus x plus x, which is equal to 4x, which is going to be equal to 36. They gave us that in the problem.