## The very beginning of function.

From this point on, we’ll start a new chapter in the algebra series – function. To do so, we need to learn the very basic concept that matters a lot in learning how the fundamental mechanism of function works.

The Cartesian Coordinate System is a two-dimensional plane used to graph points, consisting of two perpendicular lines (x and y axis) with a common origin, and it is a two-dimensional plane with two perpendicular axes (x and y), an origin where they meet, and positive and negative parts on both axes.

The system uses a pair of numbers (x,y) called coordinates to represent each point in the plane, where x is the horizontal location and y is the vertical location, and the order of the numbers matters.

In this system, the x-coordinate is positive if a point is to the right of the y-axis, negative if to the left, and zero if on the y-axis. The y-coordinate is positive if above the x-axis, negative if below, and zero if on the x-axis. The origin, located at the center, has coordinates (0,0).

When being drawn in a graph, it is divided into four parts called quadrants by the two axes. Quadrant I contains points with both positive x and y coordinates, while the other three quadrants are named in order counterclockwise.

- Quadrant I: both x and y are positive ( + , + )
- Quadrant II: x is negative and y is positive ( − , + )
- Quadrant III: both x and y are negative ( − , − )
- Quadrant IV: x is positive and y is negative ( + , − )

The four parts of the Cartesian Coordinate System are known as quadrants I, II, III, and IV and are also referred to as the first, second, third, and fourth quadrants respectively. A point in the plane is represented by a dot, which is either “graphed” or “plotted” at its location in the coordinate system.

Here’s an example – I know, my handwriting is too beautiful, right?