THE CARTESIAN COORDINATE SYSTEM

MATH-001Dr. Farhana Shaheen

THE CARTESIAN COORDINATE SYSTEM

We know that One dimensional numbers can be represented as points on a number line, and can be oriented either to the left (negative), or to the right (positive) of the origin (the zero point).

Cartesian coordinates are just the natural extension of the number line into two (or three) dimensions. In the two dimensional case, we just use two number lines (or "axes"), called the x axis and y axis, at right angles to each other. 

CARTESIAN PLANES AND COORDINATES

QUADRANTS IN CARTESIAN PLANES

QUADRANTS

POINTS IN CARTESIAN PLANE

LINEAR EQUATIONS

GRAPH OF LINEAR EQUATIONS Y = AX+B

PARABOLA

EQUATION OF PARABOLA 2xyofGraph

2xy

GRAPH OF xyxy 2

DRAW THE PARABOLA

PARABOLAS WITH DIFFERENT SHAPES

PARABOLAS IN NATURE

PARABOLAS IN LIFE

PARABOLIC BUILDING

RELATIONS ARE SET OF ORDERED PAIRS

FUNCTIONS

Functions are relations, set of ordered pairs,

in which the first elements are not repeated.

For example: A= {(1, 3), (2, 5), (3, 4), (4, 7), (5,

2)} Note: B= {(1, 1), (2, -4), (2, 4), (3, 9), (3,

-9)} is NOT a Function. (Why?)

FUNCTIONS ARE SET OF ORDERED PAIRSWHERE X-COORDINATE IS NOT REPEATEDCHECK FOR FUNCTIONS:

EXAMPLE OF A FUNCTION (Y CAN BE REPEATED)

DOMAIN AND RANGE OF A FUNCTIONTHE DOMAIN IS ALL THE X-VALUES, AND THE RANGE IS ALL THE Y-VALUES.EXAMPLE: FIND THE DOMAIN AND RANGE.

DOMAIN AND RANGE OF A RELATION

State the domain and range of the following relation. Is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} The above list of points, being a

relationship between certain x's and certain y's, is a relation.

Domain:  {2, 3, 4, 6} Range:  {–3, –1, 3, 6}

DOMAIN AND RANGE OF A FUNCTION

FUNCTIONS?

VERTICAL LINE TEST FOR GRAPH OF FUNCTIONS

CHECK FOR GRAPHS OF FUNCTIONS

GRAPHS OF FUNCTIONS?

EXAMPLE:

The set A= {(1, 1), (2, -4), (2, 4), (3, 9), (3, -

9)} is NOT a Function. These are the ordered pairs obtained from the equation

xyxy 2

FUNCTION IS AN INPUT/OUTPUT MACHINE

FUNCTION IS AN INPUT/OUTPUT MACHINE

THANK YOU