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Functions Lesson 3.8

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Definition A function is a special relation between values: The input value (domain) gives back exactly one unique Output value (range) Student Class Grade Function Grade Bilal Peter Selma Ahmad George {(B, 85), (P, 96), (S, 80), (A, 85), (G, 96)} No input value is repeated so the relation is a function

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Paris London Dubai New York Person {(A, D), (A, P), (R, N), (S, P), (S, L), (S, D), (N, D)} Ahmed Rami Sally Nancy Has visited Country Example of a relation that is not a function The inputs A and S are repeated so the relation is not a function

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function (x 2 – 1) xy DomainRange Function Notation { } 2,2,5,5,7,7, 10 { } 3,3,24,48, 99 F(x) = x 2 – 1 Output Function name input

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The Domain D and the rule of some function are given. Find the range Example D = {0, 1, 2, 3}F: x 3 – 2x; f(x) = 3 – 2x f(0) = R = {3, 1, -1, -3} 3 – 2(0) =3 f(1) =3 – 2(1) =1 f(2) =3 – 2(2) = f(3) =3 – 2(3) =-3

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Domain of the function The domain of a function is all the values that an input is allowed to take on. Give the domain of each function 1) F(x) = x 3 – 3 There are no values that I can't plug in for x. when I have a polynomial, the answer is always that the domain is all real numbers The only values that x can not take on are those which would cause division by zero. Here x can not take (1), so my domain will be All real numbers except 1 2) F(x) =

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Domain of the function The only problem I have with this function is that I cannot have a negative inside the square root. So I'll set the insides 0, and solve. The result will be my domain: 3) F(x) = x – 2 0 x 2 Then the domain is all x 2

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Consider the functions: Composite functions f(x) = 3x g(x) = x + 1and is a composite function, where g is performed first and then f is performed on the result of g. The function fg may be found using a flow diagram Examples: find the indicated value: f(g(1)) f(g(1)) g(x) x input 2 f(x) 3x = 14fg Method 1 = (1) + 1 = 2Step1: find g(1) = 3(2) = = 14Step2: find f(2) Method 2

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H.W (4, 8, 12) + (30 – 40) Even page 144, 145

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