Chapter 1 Functions

1. A relation can be represended in three ways.
a) Arrow diagram
b) Graph
c) Ordered pairs

2. Terminology

a) domain
b) codomain
c) objects
d) images
e) range

3. There's 4 types of relation, which is:
a) one to one relation
b) one to many relation
c) many to one relation
d) many to many relation

4. A funtion is said to exist if every object in the relation has one and only one image.

5. It means that only one to one and many to one relation can be said as
functions.

6. A function f, which maps x to px + q can be written as f : x = px + q . x is the
object and f(x) or px + q is the image of x under the function f.

7. A composite function is made up of two or more functions. In the diagram below, gf(x) is a
composite function where the function f maps set A to set B folows by the function g which
maps set B to set C.

8. The inverse of a funtion f, f-1, is a relation which maps every image of the function to its
object.



Example:
1) Given that f(x)=2x - 3, find the images of -2 and 1/2.

f(x) = 2x-3
f(-2) = 2(-2) -3
= - 4 - 3
= - 7

f(x) = 2x - 3
f(1/2) = 2(1/2) - 3
= 1 - 3
= - 2