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# Functions

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### Functions

1. 1. 5 6 7 8 9 1 2 3 4 5      One to One The Rule is ‘ADD 4’
2. 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. 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. 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. 5. FUNCTIONS <ul><li>Many to One Relationship </li></ul><ul><li>One to One Relationship </li></ul>
6. 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. 7. Functions - Notation The upper function is read as follows:- ‘Function f such that x is mapped onto x 2 +4
8. 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. 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. 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. 11. 2 4 14 2 Composite Functions - Arrow Diagram
12. 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. 13. Which Are Functions? (a) and (c) (a) (b) (c) (d)
14. 14. Which Are Functions? (a) and (c) (a) (b) (c) (d)
15. 15. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.