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IGCSE FM Domain/Range Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 14 th October 2015 Objectives: The specification:

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OVERVIEW This is a IGCSE FM topic only (not C1 – you don’t see domain/range until C3!) #1: Understanding of functions#2: Domain/Range of common functions (particularly quadratic and trigonometric) #3: Domain/Range of other functions #4: Constructing a function based on a given domain/range.

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RECAP :: Functions f InputOutput A function is something which provides a rule on how to map inputs to outputs. From primary school you might have seen this as a ‘number machine’. Input Output

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Check Your Understanding What does this function do? It squares the input then adds 2 to it. Q1 Q2 Q3 Q4 ? ? ? ?

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Algebraic Inputs ? ? ? ? ? ? ? ? ? ?

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Test Your Understanding ? ? ? ? A B

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Exercise 1 1 2 3 4 5 6 ? ? ? ? ? ? ? ? ? ? ? ? (exercises on provided sheet)

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Domain and Range 0 1.7 2... 3.1 1 0 2.89 4... 9.61 Inputs Outputs The domain of a function is the set of possible inputs. The range of a function is the set of possible outputs.

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Example Domain: Range: We can use any real number as the input! ? ? Sketch:

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Test Your Understanding Domain: Range: Presuming the output has to be a real number, we can’t input negative numbers into our function. The output, again, can only be positive. ? ? Sketch: ?

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Function Domain Range Function Domain Range Mini-Exercise In pairs, work out the domain and range of each function. A sketch may help with each one. Function Domain Range Function Domain Range Function Domain Range 1 2 3 Function Domain Range 4 Function Domain Range Function Domain Range 8 9 ? ? ? ? ? ? ? 5 Function Domain Range ? 6 7 ?

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Range of Quadratics A common exam question is to determine the range of a quadratic. ?

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Test Your Understanding ? ?

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Range for Restricted Domains Some questions are a bit jammy by restricting the domain. Look out for this, because it affects the domain! ?

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Test Your Understanding ? ?

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Range of Trigonometric Functions DomainRange Suppose we restricted the domain in different ways. Determine the range in each case (or vice versa). Ignore angles below 0 or above 360. ? ? ?

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Range of Piecewise Functions It’s a simple case of just sketching the full function. Graph ?Range ?

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Test Your Understanding Graph ?Range ?

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Exercise 2 1 2 3 4 5 ? ? ? ? ? ? ? ? ? ? ? (exercises on provided sheet)

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Exercise 2 6 7 8 ? ? ? ? ? (exercises on provided sheet)

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Exercise 2 910 ? ? ? ? ? (exercises on provided sheet)

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Exercise 2 1113 12 ? ? ? (exercises on provided sheet)

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Constructing a function from a domain/range June 2013 Paper 2 ? ?

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Constructing a function from a domain/range Sometimes there’s the additional constraint that the function is ‘increasing’ or ‘decreasing’. We’ll cover this in more depth when we do calculus, but the meaning of these words should be obvious. ?

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Exercise 3 1 2 3 4 5 ? ? ? ? ? (exercises on provided sheet)

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