Delta y just means change in y.

Delta, this triangle, means change, change in y.

One unit down means the y decreases by 1.

We doubled Y, so that's what it means when something varies directly

So that means that the image of f is equal to y.

Well, if Y is a basis, then that means that it spans V.

So if y varied directly with x it literally means that y is equal to some constant multiple of x, or if you divide both sides of this by x it means that y over x is equal to k so the ration between y and x is a constant.

And rise just means how much do you change in y, run means how much do you change in x.

So for example, Texas has at one point decided that what it means to marry a man is to mean that you don't have a Y chromosome, and what it means to marry a woman means you have a Y chromosome.

That means when x is equal to 0, y is equal to negative 3.

When x is equal to 0, then that means y is going to be

And that really just means relating it to, or associating with another member of y.

Now let's think a little bit about what x to the 2 and y to the 2 mean. x to the 2 just means 1 over x squared, y to the 2 just means 1 over y squared so let's rewrite it like that, this is the same thing as, 1 over x squared times 1 over y squared

Y Y Yes.

If you see just an x or y that generally means that you're dealing with a variable term.

So that means that if I change x by positive 1 that y goes down by negative 2.

That means when I move 1 in the x direction, I move up 2 in the y direction.

What's the anti derivative of y, the function y or y d y.

Y y yeah, right.

But then we have a y. y to the first. y squared. y to the third. y to the fourth. y to the fifth.

Which means if we go 1 in the x direction, we're going to go up 4 in the y.

And then y times y, well that's just y squared,

Y and a y squared.

Here f of y is square root of y squared d y.

Just as a bit of a review, that means equations of lines in the form of y is equal to mx plus b where m is the slope and b is the y intercept.

Whenever you see a y sub 1 or an x sub 1, that means you're actually dealing with a constant term.

So that means that this is the Laplace Transform of y, is equal to 9 times the Laplace Transform of what?

Square root of y squared is y.

log of y is 1 over y.

Square root of y squared is y.

Change in y would be this y.

If and only if for all y, for every y that is a member of our set y there exists a unique I can actually write that like that means there's exists a unique x for the or let me write this way there exists a unique solution to the equation f of x is equal to y.

The y terms become 4 times y minus 2 squared. y minus 2 squared.

And then finally, y to the sixth over y to the fifth, that's y to the 6 minus 5 power, which is just y to the first power, or just y, so times y.

And then I have to worry about the y terms, times y squared times another y squared times another y squared.

So this just means, I don't care what your y is, x is just always going to be equal to negative 2.

So if we say that y is equal to a function of x, all that means is, you give me an x.

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