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www.le.ac.uk Introduction to functions Department of Mathematics University of Leicester

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Content FunctionsIntroductionFunctions as graphsWorking with functionsMappings

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Introduction Functions Mappings Functions as graphs Working with functions Next Intro

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Mappings Next Functions Mappings Functions as graphs Working with functions Intro

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Domain & Range Next Functions Mappings Functions as graphs Working with functions Intro

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Functions Next Functions Mappings Functions as graphs Working with functions Intro

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One-to-one A mapping that maps one element to one element is called a one-to-one function. Next Functions Mappings Functions as graphs Working with functions Intro

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Many-to-one A mapping that maps more than one element to one element is called a many-to-one function. Next Functions Mappings Functions as graphs Working with functions Intro

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One-to-many A mapping that maps one element to one or more elements is not a function. Next Functions Mappings Functions as graphs Working with functions Intro

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Question... Which of these is a many-to-one function? None of the above Functions Mappings Functions as graphs Working with functions Intro

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Question... What is this: ? One-to-One One-to-ManyMany-to-One Functions Mappings Functions as graphs Working with functions Intro

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Question... What is this: ? One-to-One One-to-ManyMany-to-One Functions Mappings Functions as graphs Working with functions Intro

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Working with functions Next Functions Mappings Functions as graphs Working with functions Intro

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Examples Next Functions Mappings Functions as graphs Working with functions Intro

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Your turn 3 8 9 27 None of the above Functions Mappings Functions as graphs Working with functions Intro

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Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

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Functions as graphs Domain Range Next Functions Mappings Functions as graphs Working with functions Intro

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Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

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Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

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Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

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Question... Functions Mappings Functions as graphs Working with functions Intro What kind of mapping is this? One-to-0neOne-to-manyMany-to-one

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Conclusion Functions Mappings Functions as graphs Working with functions Next Intro You should now be able to: Find the range and domain of a mapping. Categorise mappings (one-to-one, etc.) Do simple computations with functions. When you feel comfortable move on to composition of functions.

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Functions Relation such that each element x in a set A maps to EXACTLY ONE element y in a set B Set A: Domain = set of all numbers for which the formula.

Functions Relation such that each element x in a set A maps to EXACTLY ONE element y in a set B Set A: Domain = set of all numbers for which the formula.

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