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One to One. . 1 2 3 4 5. 5 6 7 8 9. . . . . The Rule is ‘ADD 4’. Paris London Dubai New York Cyprus. Ahmed Peter Ali Jaweria Hamad. . . . . Has Visited. There are MANY arrows from each person and each place is related to MANY

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5 6 7 8 9

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

  2. Paris London Dubai New York Cyprus Ahmed Peter Ali Jaweria Hamad     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. Person Has A Mass of Kg  Bilal Peter Salma Alaa George Aziz 62 64 66      In this case each person has only one mass, yet several people have the same Mass. This is a MANY to ONErelationship

  4. Is the length of cm object  Pen Pencil Ruler Needle Stick  14 30    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! x2x+1 A B 0 1 2 3 4 1 2 3 4 5 6 7 8 9 Image Set (Range) Domain Co-domain

  7. Functions - Notation The upper function is read as follows:- ‘Function f such that x is mapped onto x2+4

  8. Lets look at some function Type questions ( ) = + ( ) = - 2 2 f x x 4 a n d g x 1 x ( ) F i n d f 2 ( ) F i n d g 3 If = 8 = -8 2 2 3 3

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

  10. Thus = 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 Add 2 square Multiply by 3

  11. Composite Functions - Arrow Diagram 2 14 4 2

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

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

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

  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.

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