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Functions

on Jun 07, 2013

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FunctionsPresentation Transcript

• 5678912345The Rule is ‘ADD 4’
• AhmedPeterAliJaweriaHamadParisLondonDubaiNew YorkCyprusHas VisitedThere are MANY arrows from each person and each place is related to MANYPeople. It is a MANY to MANY relation.
• 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
• Is the length of1430PenPencilRulerNeedleStickcm objectHere one amount is the length of many objects.This is a ONE to MANY relationship
• FUNCTIONS• Many to One Relationship• One to One Relationship
• Domain Co-domain01234123456789Image Set (Range)x2x+1A B
• f : x  x2+4f(x)=x2+4The upper function is read as follows:-‘Function f such that x is mapped onto x2+4
• 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
• 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
• 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
• g ffg(x)x23x + 23x2+ 224 142
• 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
• (a)(b)(c) (d)(a) and (c)
• (a)(b)(c) (d)(a) and (c)
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