First bit of business for the day, Algebra II!

So, here’s the daily note card!

Covered relations and functions today. Fun facts!

- Relations
- The coordinate plane is specifically the Cartesian coordinate plane. Composed of the X (horizontal) axis and the Y (vertical) axis.
- A relation is any set of ordered pairs. Usually represented as (X, Y), or as an example, (5, 10).
- The X value is known as the domain, while the Y value is known as the range.

- Function
- A function is defined as a type of relation in which each element of the domain is paired with ONE element of range.
- Examples:
- One-To-One: ((-3, 1), (0, 2), (2,4)),
- Not One-To-One: ((-1, 5), (1, 3), (4, 5))
- Not even a thing: ((5, 6), (-3, 0), (-3, 6))

- Example 2 is a function because each X value only corresponds to one Y value. It just so happens that in two cases, that Y value is 5.
- Example 3 is invalid because an x value (-3) is attached to 2 Y values (0 and 6).

- Examples:
- The Vertical Line Test
- The test can be summarized as follows: If you graph something, if it’s a function than you can draw a vertical line at any point on the graph, and it will only pass through one point.
- If it passes through more than one point, whatever you just graphed isn’t a function.

- F(X)
- When describing a function as an equation, you might do, for example, Y= 4X+4.
- In some cases, people will write it as F(X) = 4x + 4
- This doesn’t change the equation at all, F(X) is meant to be read as “F of X”, shorthand for “function of X”. It’s just meant to say that the equation is the function of X, how things are working.

- A function is defined as a type of relation in which each element of the domain is paired with ONE element of range.

Next up, Game Design! So, what did I do today? Big things!

Very big things!

I’m being serious here.

…

The game finally lives up to it’s name! You can make guesses, and it will tell you how many bulls (letters in the right place) and cows (letters in the wrong place) you get! It’s still a touch buggy, and needs improvements, like not taking guesses of the wrong length and such, but this is a gigantic leap!

Anyways, last was economics. Covered the types of economies today. Traditional, Command, Market, and Mixed.

- Traditional: People are assigned certain economic roles, which makes for a rather stable life. However, it is rigid, stagnant, and tends to have a low quality of life.
- Command: Can change massively very quickly, and many basic needs are available for free or cheap. On the downside, a command economy does not meet the desires of consumers, tends to lack incentives to work, and requires a massive bureaucracy.
- Market: Adjusts to change gradually, individual freedom plenty, little government interference, large variety of stuff. On the other hand, only productive things are rewarded. Old, sick, and young are at a disadvantage. Public services are at a disadvantage if they aren’t profitable (road building), and the competition between businesses puts jobs and profits at risk.
- Mixed: A combination of the above three. Has advantages and disadvantages of the above three, with some sacrifices to accommodate.