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# Functions

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### Functions

1. 1. 5678912345The Rule is ‘ADD 4’
2. 2. AhmedPeterAliJaweriaHamadParisLondonDubaiNew YorkCyprusHas VisitedThere are MANY arrows from each person and each place is related to MANYPeople. It is a MANY to MANY relation.
3. 3. BilalPeterSalmaAlaaGeorgeAziz626466Person Has A Mass of KgIn this case each person has only one mass, yet several people have the sameMass. This is a MANY to ONE relationship
4. 4. Is the length of1430PenPencilRulerNeedleStickcm objectHere one amount is the length of many objects.This is a ONE to MANY relationship
5. 5. FUNCTIONS• Many to One Relationship• One to One Relationship
6. 6. Domain Co-domain01234123456789Image Set (Range)x2x+1A B
7. 7. f : x  x2+4f(x)=x2+4The upper function is read as follows:-‘Function f such that x is mapped onto x2+4
8. 8. Lets look at some functionType questionsIff(x) = x2 + 4 and g(x) = 1 − x2Find f(2)Find g(3)f(x) = x2+ 42 2 = 8 g(x) = 1 − x23 3= -8
9. 9. Consider the function f(x) = 3x − 1 We can consider this as two simplerfunctions illustrated as a flow diagramMultiply by 3 Subtract 13x 3x − 1xConsider the function f : x  (2x + 5)2xMultiply by 2 Add 52x 2x + 5Square(2x + 5)2
10. 10. f : x  3x + 2 and g(x) : x  x2Consider 2 functionsfg is a composite function, where g is performed first and then f is performedon the result of g.The function fg may be found using a flow diagramxsquarex2Multiply by 33x2Add 23x2+ 2g fThus fg = 3x2+ 2
11. 11. g ffg(x)x23x + 23x2+ 224 142
12. 12. Consider the function f(x) = 5x − 23Here is its flow diagramxx5x5 -2 f(x) = 5x − 23Draw a new flow diagram in reverse!. Start from the right and go left…Multiply by 5 Subtract 2 Divide by threeMultiply by threeAdd twoDivide by 5x3x3x +23x +25f−1(x) = 3x + 25And so
13. 13. (a)(b)(c) (d)(a) and (c)
14. 14. (a)(b)(c) (d)(a) and (c)
15. 15. This powerpoint was kindly donated towww.worldofteaching.comhttp://www.worldofteaching.com is home to over athousand powerpoints submitted by teachers. This is acompletely free site and requires no registration. Pleasevisit and I hope it will help in your teaching.