1. Relations and functions
By Nicolas Mastandrea
Relations and functions

2. The relation
A relation is just a set of ordered pairs. There is absolutely nothing special at all about the numbers that are in a relation. In other words, any bunch of numbers is a relation so long as these numbers come in pairs.

3. The function
In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value.

4. Categories of functions
Constant function
Direct variation linear function
Partial variation linear function
Rational function
Quadratic function

5. The constant function The rate of change is constant and equal to 0.
On a cartesian graph, it is a straight horizontal line parallel to the x-axis.
Rules: y=b or f(x)=b

6. Direct variation linear function
The rate of change is constant!
The y variable is proportional to the x variable
The Cartesian graph is a straight line passing through the origin, and is not parallel to an axis.
Rules: y=ax or f(x)=ax

7. Partial variation linear function
The rate of change is constant!
The y variable is not proportional to the x variable.
The Cartesian graph is a straight line that does not pass through the origin and is not parallel to an axis.
Rules: y=ax+b or f(x)=ax+b

8. The rational function The rate of change is not constant.
The product of the variables is constant.
The Cartesian graph is a curve that gradually approaches the axes.
Rules: y= a/x or f(x)= a/x

9. Quadratic function The rate of change is not constant
Y is proportional to the square of x
The complete graph is a curve called a parabola.
Rules: y = ax2+bx+c or f(x) = ax2+bx+c