1.2 functions and function notation worksheet answers

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Functions and Function Notation – Worksheet

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MCR3U

Jensen 1) For each function, determine 𝑓( 4 ), 𝑓(− 5 ), and 𝑓 − ! !

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a) 𝑓𝑥 = ! ! 𝑥+ 11 b) 𝑓𝑥 = 3 𝑥!+ 2 𝑥+ 1 c) 𝑓𝑥 = 2 (𝑥+ 4 )! d) 𝑓𝑥 =− 6 e) 𝑓𝑥 = ! ! f) 𝑓𝑥 = 𝑥+ 5

2) If 𝑓𝑥 =𝑥!+ 2 , state the following. a) 𝑓( 1 ) b) 𝑓( 0 ) c) 𝑓( 2 ) d) 𝑓(− 2 ) e) 𝑓( 3 ) f) 𝑓 ! ! 3) State 𝑓 4 for each of the following functions. a) 𝑓𝑥 = 4 + 5 𝑥 b) 𝑓𝑥 =𝑥!− 6 c) 𝑓𝑡 = 9 −𝑡 d) 𝑓𝑥 = 10 e) 𝑓𝑧 =𝑧! f) 𝑓𝑥 = 8 ( 5 −𝑥) g) 𝑓𝑥 = ! ! h) 𝑓𝑥 = 13 −𝑥 i) 𝑓𝑡 = ! !!

5) Show each set of data in a mapping diagram. Then state if the relation is a function. a) { 1 , 4 , 2 , 1 , 3 ,− 2 , 4 ,− 5 , 5 ,− 8 , 6 ,− 11 , 7 ,− 14 , 8 ,− 17 } b) {− 3 , 4 , − 2 ,− 1 , − 1 ,− 4 , 0 ,− 5 , 1 ,− 4 , 2 ,− 1 } c) {− 5 , 6 , − 4 , 9 , − 3 , 1 , − 5 ,− 6 , 1 ,− 2 , 3 , 8 , 8 , 8 } d) { 9 , 9 , 7 , 9 , 5 , 9 , 3 , 9 } 6) State the domains of the following functions a) 𝑓𝑥 = 8 −𝑥 **b) ** 𝑓𝑥 = !!!! (!!!)(!!!)

Answers 1) a) !" !

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!"! !" **b) ** 57, 66, 1 c) 128, 2, !"" ! d) -‐ 6, -‐6, -‐6 e) ! !

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! !

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! ! f) 3, 0, !" ! 2) a) 3 b) 2 c) 6 d) 6 e) 11 **f) ** ! ! 3) a) 24 b) 10 c) 5 d) 10 e) 64 f) 8 g) ! ! h) 3 i) ! !" 4) a) { 1 , 1 , 2 , 4 , 3 , 9 , 4 , 16 } this relation is a function b) {− 5 , 11 , − 4 , 6 , − 2 ,− 4 , 0 ,− 14 , 2 ,− 24 } this relation is a function c) {− 4 , 6 , 3 , 6 , 1 , 6 , 5 , 6 } this relation is a function d) {− 1 ,− 3 , 1 ,− 3 , 1 , 0 , 3 , 2 , 5 , 2 } this relation is NOT a function 5) a) function b) function c) Not a function d) function 6) a) {𝑋∈ℝ|𝑥≤ 8 } b) {𝑋∈ℝ|𝑥≠ 1 ,𝑥≠− 3 }

1.2 Functions and Function Notation – WorksheetMCR3UJensen1)For each function, determine࠵?(4),࠵?(−5), and࠵?−!!.a)࠵?࠵?=!!࠵?+11b)࠵?࠵?=3࠵?!+2࠵?+1c)࠵?࠵?=2(࠵?+4)!d)࠵?࠵?=−6e)࠵?࠵?=!!f)࠵?࠵?=࠵?+5

2)If࠵?࠵?=࠵?!+2, state the following.a)࠵?(1)b)࠵?(0)c)࠵?(2)d)࠵?(−2)e)࠵?(3)f)࠵?!!3)State࠵?4for each of the following functions.a)࠵?࠵?=4+5࠵?b)࠵?࠵?=࠵?!−6c)࠵?࠵?=9−࠵?d)࠵?࠵?=10e)࠵?࠵?=࠵?!f)࠵?࠵?=8(5−࠵?)g)࠵?࠵?=!!h)࠵?࠵?=13−࠵?i)࠵?࠵?=!!!