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An Introduction to Functions
Slideshow 22, Mathematics Mr Richard Sasaki, Room 307
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Objectives To learn what a function is and necessary notation
To apply functions to sets of numbers Understanding basic rules and restrictions on functions
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Functions A function is a process that changes something. We input something, it is processed and then an output is left. Process Input Output 12 48 Γ4
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π( ) π₯ = 2π₯+4 Notation A function of something is denoted asβ¦
π( ) π₯ = 2π₯+4 For a function of a variable π₯, we would writeβ¦ We can state what we want the function to do here. So this means for a number π₯, the function doubles it and then adds 4 to it.
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2Β·4+4 12 π( ) π₯ = 2π₯+4 π( ) 4 = = Specific Values Try the worksheet!
Letβs try inserting the value 4. π( ) π₯ = 2π₯+4 π( ) 4 = 2Β·4+4 = 12 Basically this is the same as substituting π₯=4 into the function.
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Answers 26 -10 -5 -4 π(π₯) = 3π₯ β 4 π(3)=5, π(4)=8, π(5)=11,
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Rules for Functions A function must work for all numbers it was designed for. But this doesnβt put restrictions on results missing. This is not allowed, an inputted value must have exactly 1 result. It is fine if not every number is included as an answer. Weβll look at this in more detail in later lessons.
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What are sets? Sets are the basis of mathematics. They are basically a collection of things. For example, the set of colours in the rainbow is {π
ππ, ππππππ, ππππππ€, πΊππππ, π΅ππ’π, πΌπππππ, ππππππ‘}. A set is a group of elements (eg: Red) in curly brackets {ππππ π‘βππ }. They must be separated by commas. Order has no meaning.
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Answers 6 Yes 52 {1, 2, 3, 4, 5, 6} π(π₯)=2π₯ β4 to 11 (or 15)
{5, 6, 7} Yes β4 to 11 (or 15) No, π(4) can only be one value. Yes it is. 5 π(π₯)=20π₯ π(π₯)=2π₯ π(6)=120ππ Because it is inaccurate. A 20 year old is not 4m tall. Yes Eg: π(π₯)=7π₯+110 52 π(π₯)=20π₯ Negative numbers or very high ones Hearts, Diamonds, Clubs, Spades π(40)=800ππ or 8π Approx {0, β¦, 50} Negative numbers cannot be entered (without including imaginary numbers).
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