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Functions and Relations Objective: To find values of, graph, and determine the domain and range of relations as well as determine which relations are functions.

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by Gavin McGerald2 Relations A relation is any set of ordered pairs. The ordered pairs are made up of a domain (typically x) which is mapped to a range (typically y or f(x)).

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by Gavin McGerald3 What is a mapping? Domain -2 3 5 Range 0 2 4 7 In this relation {(-2, 2), (3, 0), (3, 7), (5, 0), (5, 2), (5, 4)} the domain {-2, 3, 5} is mapped to the range {0, 2, 4, 7}

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by Gavin McGerald4 What is a function? A function is a relation where each element of the domain is paired with exactly one element of the range.

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by Gavin McGerald5 Relations that are: Functions {(2,3), (3,1), (1,1)} 23 14 0 Not Functions {(3,2), (1,3), (1,1)} 23 14 0 y x y x

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by Gavin McGerald6 How can you tell if a graph of a relation is a function? The vertical line test. A relation is a function if and only if no vertical line intersects its graph more than once.

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by Gavin McGerald7 Terminology f: x 3x is read the function f that assigns x to the number 3x Function notation f(x) function of x or f of x

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by Gavin McGerald8 Try These! g: x 2x – 3 1.g(3) 2.g(½) 3.g(-3) 4.g(h + 1) 5.g(x + ½) Solutions 2(3) – 3 = 3 2(½) – 3 = -2 2(-3) – 3 = -9 2(h + 1) – 3 = 2h – 1 2(x + ½) – 3 = 2x – 2

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by Gavin McGerald9 Try A Few More! Determine if each relation is a function. 1.{(2, 3), (-1, 0), (1, 3), (0, 2)} 2. 3. 4. y = 3x – 2 5. y 2 = x y x y x

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by Gavin McGerald10 Solutions 1.Yes 2.Yes 3.No, vertical line test 4.Yes, its an equation for a line and thus a vertical line will only pass through it once. 5.No, If x = 4 y could equal 2 or - 2

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