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5 67895 6789 1234512345 The Rule is ADD 4

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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.

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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

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

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FUNCTIONS Many to One Relationship One to One Relationship

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DomainCo-domain 0 1 2 3 4 1 2 3 4 5 6 7 8 9 Image Set (Range) x 2x+1 AB

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The upper function is read as follows:- Function f such that x is mapped onto x 2 +4

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Lets look at some function Type questions If f x x 2 4andg x 1 x 2 Findf 2 Findg 3 2 2 = 8 3 3 = -8

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

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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 =

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2 4 14 2

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

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(a) (b) (c) (d) (a) and (c)

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(a) (b) (c) (d) (a) and (c)

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