Functions

Analytic plane

x-axis

y-axis

origin

1st quadrant

(+,+)

2nd quadrant

(-,+)

3rd quadrant

(-,-)

4th quadrant

(+,-)

Ordered Pair:

Given that a and b are any two elements, (a,b) is called an ordered pair where a is first component and b is second component.

Example:

(5, -1)

(abu, elham)

(a, b)

(square, triangle)

(adhaser, 165 cm)

(emanuel, ?)

Example:

y = x – 2. Give four example for the ordered pair (x, y).

Equality of ordered pairs

Let (m, n) and (p, q) be two ordered pairs.

(m, n) = (p, q) if and only if m = p and n = q.

Example: find x and y if (x + 1, 6) = (8, 2y – 4)

Notations of intervals:

Let a and b be real numbers.

A = [a, b] denotes the set of all real numbers between a and b (a and b are included).

a b

a b

A = (a, b) denotes the set of all real numbers between a and b (a and b are excluded).

A = [a, b) denotes the set of all real numbers between a and b (a is included and b is excluded).

a b

a b

A = (a, b] denotes the set of all real numbers between a and b (a is excluded and b is included).