1. Types of functions and maximal domains
One-to-one and many-to-one functions
Functions are relations that are one-to-one or many-to-one.
•For all functions, no two ordered pairs have the same x value.
•One way to identify if a relation is a function is to draw a graph
of the relation and apply the vertical line test.
•The graph of a one-to-one function can be crossed only once by
any vertical or horizontal line.

2. A function that is not one-to-one is
many-to-one.
Maximal (implied) domain
If the domain of the function is not stated in the rule it is understood
(implied) that the maximum possible domain (the largest subset of R)
for that function is intended.
Example 1.

4. Hybrids
These are functions for which different rules apply for different parts of the
domain.
Example 2.

5. This can be done
manually or by calculator
Odd and even functions
Odd fns are symmetrical through the origin
Note: For odd fns the left half of the plane
looks like the mirror image of the right half
of the plane, only upside down.

6. Exercise 1C 1,2 ESO, 4-7 ESO, 9 -14 ESO