Function-Modelling.pdf

Activity 1: Guess the “function” 𝒚 = 𝟐𝒙 x y x y 2 4 5 10 -8 -16 Activity 1: Guess the “function” 𝒚=𝒙+𝟏 x...

Activity 1: Guess the “function” 𝒚 = 𝟐𝒙 x y x y 2 4 5 10 -8 -16 Activity 1: Guess the “function” 𝒚=𝒙+𝟏 x y x y 7 8 9 10 11 12 Do you think this is “functional”? 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,– 1), ( 4, 2), (4, –2), (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. 𝒙=𝟑 b. 𝒙 = −𝟓 c. 𝒙 = −𝟐 d. 𝒙=𝟗 Evaluate 𝒇 𝒙 = 𝟐𝒙 + 𝟕 𝒊𝒇 𝒙 = −𝟓 𝒇 𝒙 = 𝟐𝒙 + 𝟕 𝒇 −𝟓 = 𝟐(−𝟓) + 𝟕 𝒇 −𝟓 = −𝟏𝟎 + 𝟕 𝒇 −𝟓 = −𝟑 Evaluate 𝒇 𝒙 = 𝟐𝒙 + 𝟕 𝒊𝒇 𝒙 = −𝟐 𝒇 𝒙 = 𝟐𝒙 + 𝟕 𝒇 −𝟐 = 𝟐(−𝟐) + 𝟕 𝒇 −𝟐 = −𝟒 + 𝟕 𝒇 −𝟐 = 𝟑 Evaluate 𝒇 𝒙 = 𝟐𝒙 + 𝟕 𝒊𝒇 𝒙 = 𝟗 𝒇 𝒙 = 𝟐𝒙 + 𝟕 𝒇 𝟗 = 𝟐(𝟗) + 𝟕 𝒇 𝟗 = 𝟏𝟖 + 𝟕 𝒇 𝟗 = 𝟐𝟓 ASSESSMENT 1.1 I. Determine if the given represents a Function or Not. 1. 4. 2. 5. 3. II. Evaluate the given function 1. 𝑤 𝑡 = −2𝑡 + 1 ; 𝐹𝑖𝑛𝑑 𝑤 7 2. ℎ 𝑛 = −2𝑛2 + 4; 𝐹𝑖𝑛𝑑 ℎ −4 3. 𝑤 𝑎 = 𝑎 + 3; 𝐹𝑖𝑛𝑑 𝑤(6)