Function Modelling PDF
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Sto. NiΓ±o Mactan Montessori School
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This document contains learning material on functions, including activity examples and questions. It goes through defining functions, evaluating functions and identifying examples of functions by using diagrams and graphs. The examples demonstrate the evaluation of function parameters.
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Activity 1: Guess the βfunctionβ π = ππ x y x y 2 4 5 10 -8 -16 Activity 1: Guess the βfunctionβ π=π+π x...
Activity 1: Guess the βfunctionβ π = ππ x y x y 2 4 5 10 -8 -16 Activity 1: Guess the βfunctionβ π=π+π x y x y 7 8 9 10 11 12 Do you think this is βfunctionalβ? x y x y 3 -1 3 -5 5 -1 So, what is a function? DIAGRAM Which is NOT a function? One-to-many Function correspondence One-to-one correspondence NOT a FUNCTION Function Function Many-to-one One-to-one correspondence correspondence SET NOTATION Determine whether each relation is a function. 1. {(2, 3), (3, 0), (5, 2), (4, 3)} 2 3 f(x) 3 0 f(x) 5 2 f(x) YES, every domain is different! 4 3 f(x) Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} 4 1 f(x) 5 2 f(x) NO, 5 f(x) 3 5 is paired with 2 numbers! 6 6 f(x) 1 9 f(x) Which set of ordered pairs represents a function? NOT A). {(1,1), (1,β 1), ( 4, 2), (4, β2), (9, 3) } NOT B). {(3, 4),(3, 5),(3, 6),(3, 7), (3, 8) } FUNCTION C). {(2, 4), (3, 4), (4, 4,), (5, 4), (6,4) } NOT D). {(1, 2), (2, 3), (3,4), (4,5), (4, 6) } GRAPH Function or NOT? VERTICAL LINE TEST A graph represents a function if and only if each vertical line intersects the graph at most once Function Function or NOT? Function Function or NOT? NOT Function Evaluating Functions: Integers If a. π=π b. π = βπ c. π = βπ d. π=π Evaluate π π = ππ + π ππ π = βπ π π = ππ + π π βπ = π(βπ) + π π βπ = βππ + π π βπ = βπ Evaluate π π = ππ + π ππ π = βπ π π = ππ + π π βπ = π(βπ) + π π βπ = βπ + π π βπ = π Evaluate π π = ππ + π ππ π = π π π = ππ + π π π = π(π) + π π π = ππ + π π π = ππ ASSESSMENT 1.1 I. Determine if the given represents a Function or Not. 1. 4. 2. 5. 3. II. Evaluate the given function 1. π€ π‘ = β2π‘ + 1 ; πΉπππ π€ 7 2. β π = β2π2 + 4; πΉπππ β β4 3. π€ π = π + 3; πΉπππ π€(6)