Let x be the amount of money.

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

Well then I could say, let x be the price

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

Let me call this X.

let me, this is x.

And what do we get? x squared plus 3x plus 6 minus x squared let me be very careful this is minus x squared plus x.

let me call them x sub 1, x sub 2, and x sub 3.

let me call u is equal to delta x over x.

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 do my x axis.

Let me call that vector x.

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 in Part a, let's let x be the number bus can seat.

Let me factor an x squared out.

Let me just not take an x.

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

let me copy and paste cosine(x) so, cosine (x) right up here

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.

So let me draw a little table here, so this will be X and lets call this f(x) and we could set, our Y values to be equal to f(x)

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.

So let me write this, change in x, delta x is equal to 3.

Let me draw the x axis, y axis.

So let me draw my f of x.

So let's let x equal days after Monday.

Let me draw my x axis right here.

Let me just write it x, y, z.

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

And then let me draw..So everywhere except x 2, it's equal to x². So let me draw it like this, this is gonna be a parabola, it looks something like this...

Let me define my transformation of x, of any x, to be equal to the matrix 1 minus 1, 2, 0 times whatever vector x. So times x1, x2.

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.

When our delta x is equal to let me write it this way, delta x.

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

Let me rewrite it in maybe terms of x.

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).

This would be equal to x plus 2 let me write it this way it would be equal to, if you divide this by 2, it becomes an x.

Let me write it up here. x squared minus x minus 6 is equal to 0.

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

Times the vector, let me just call this vector x, that right there is vector x.

Let's say you say I want f of x to be within point let me do a different color I want f of x to be within 0.5 of 2.

Let me switch back to minus, green that's x plus delta x to the n, so minus x to the n power.

Let me do h of x in a different color.

And it would be. x over x times x.