This document discusses different types of relationships between inputs and outputs in functions: - One-to-one relationships have unique outputs for each input. - Many-to-one relationships have multiple inputs mapping to the same output. - One-to-many relationships have a single input mapping to multiple outputs. - Many-to-many relationships have multiple inputs each mapping to multiple outputs. It also covers function notation, composite functions using flow diagrams, and inverse functions obtained by reversing the arrows in a function diagram.

1. 5 6 7 8 9 1 2 3 4 5      One to One The Rule is ‘ADD 4’

2. Ahmed Peter Ali Jaweria Hamad Paris London Dubai New York Cyprus     Has Visited There are MANY arrows from each person and each place is related to MANY People. It is a MANY to MANY relation.

3. Bilal Peter Salma Alaa George Aziz 62 64 66 Person Has A Mass of Kg       In this case each person has only one mass, yet several people have the same Mass. This is a MANY to ONE relationship

4. Is the length of 14 30 Pen Pencil Ruler Needle Stick cm object      Here one amount is the length of many objects. This is a ONE to MANY relationship

5. FUNCTIONS Many to One Relationship One to One Relationship

6. Function - Domain and Range! Domain Co-domain 0 1 2 3 4 1 2 3 4 5 6 7 8 9 Image Set (Range) x  2x+1 A B

7. Functions - Notation The upper function is read as follows:- ‘Function f such that x is mapped onto x 2 +4

8. If 2 2 = 8 3 3 = -8 Lets look at some function Type questions f  x   x 2  4 a n d g  x   1  x 2 F i n d f  2  F i n d g  3 

9. Flow Diagrams We can consider this as two simpler functions illustrated as a flow diagram Multiply by 3 Subtract 1 Multiply by 2 Add 5 Square

10. Compound(Composite) Functions Consider 2 functions is a composite function, where g is performed first and then f is performed on the result of g . The function fg may be found using a flow diagram square Multiply by 3 Add 2 Thus =

11. 2 4 14 2 Composite Functions - Arrow Diagram

12. Inverse Functions Draw a new flow diagram in reverse!. Start from the right and go left… Consider the function Here is its flow diagram 5 5 -2 Multiply by 5 Subtract 2 Divide by three Multiply by three Add two Divide by 5 3 3 +2 3 +2 5 And so

13. Which Are Functions? (a) and (c) (a) (b) (c) (d)

14. Which Are Functions? (a) and (c) (a) (b) (c) (d)

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