FUNCTIONS & RELATIONSHIPS 1 Chapter 5, Page 62

Input and Output Values Flow Diagram: Table: Symbols: 3x + 2 Input values Output values -1 1 2

Example 1: CONSIDER THE TABLE OF INPUT VALUES AND OUTPUT VALUES Input number (x) 1 2 3 4 5 6 102 Output number (y) 9 13 17 a) Rule in words: To calculate the output value, you multiply the input value by 4 and then add 1 b) Formula: y = 4𝑥 +1 c) Determine 𝑦 if 𝑥 = -7 y = 4(-7) + 1 y = - 28 + 1 y = - 27 d) Determine 𝑥 if 𝑦 = 53 We do the reverse process if we have been given y and are looking for x 53 – 1 = 52 52 ÷ 4 = 13 ∴ 𝑥 = 13

Example 2: CALCULATE Y IF X IS EQUAL TO: b) 𝑥 = -2 𝑦 = 2𝑥 + 3 𝑦 = 2(-2) + 3 𝑦 = - 4 + 3 𝑦 = -1

Example 3: complete the table; write a rule in words; write an algebraic rule Input (x) 1 2 3 4 5 6 17 Output (y) 8 27 64 2197 8000 Rule in words: Cube the input number to get the output number Algebraic rule (formula): y = x3 DO: Exercise 5.1 Page 64 # 1RHS; 2a; 3b; 4; 5; 6

EXERCISE 5.1: ANSWERS 1b) 3; 5; 7 Add two d) -32; 64; -128 Multiply each term by -2 f) 277; 138,5; 69.25 Divide each term by 2

2a) i) y = 3x – 5 y = 3(-3) – 5 y = -9 - 5 y = -14 b) ii) y = 3x - 5 y = 3(-2) - 5 y = - 6 – 5 y = - 11 2a) iii) y = 3x – 5 y = 3(-1) – 5 y = -3 - 5 y = -8 b) iv) y = 3x - 5 y = 3(0) - 5 y = 0 – 5 y = - 5

2a) v) y = 3x – 5 y = 3(1) – 5 y = 3 - 5 y = -2 3b) i) ii) Divide the input number by two iii) y = 𝑥 2 Input (x) -100 -76 -54 -26 -52 32 Output (y) -50 -38 -27 -13 16

4a) b) The number of pegs is one more than the number of clothing items c) p = c + 1 5a) Diagram 4 Diagram 5 b) c) y = 5x + 1 # of clothing items (c) 1 2 3 4 5 11 50 69 n # of pegs (p) 6 12 51 70 n + 1 Diagram (x) 1 2 3 4 5 6 Number of matches (y) 11 16 21 26 31

6a) b) d = 2p + 2 c) l = 4p + 1 Pattern number (p) 1 2 3 4 20 63 P Number of dots (d) 6 8 10 42 128 2p + 2 Number of lines (l) 5 9 13 17 81 253 4p +1 DO: Ex 5.2 pg 66 #1; 2; 3b,c; 4; 5a i, v, vi

Exercise 5.2: answers 1a) 1b) x -5 -2 13 29 57 m y y = 4x -2 -10 50 114 226 4m -2 x -5 -2 13 29 57 N y y = 7 - 2x y = 7 – 2(-5) y = 7 + 10 y = 17 11 -19 -51 -107 7- 2n

2a) b) Subtract 3 from the output number; then divide by two to get the input number. c) y = 2x + 3

3b) y = 4x – 3 3c) y = 3x - 5 Input (x) 5 6 7 8 9 Output (y) 17 21 25 29 33 Input (x) 5 6 7 8 9 Output (y) 10 13 16 19 22

4a) P = l + b + l + b = 34 + 19 + 34 + 19 = 106cm P = 2l + 2b = 2(34) + 2(19) = 68 + 28 = 2 (32 + 19) = 2(53) = 106cm 4b) 328 – 62 – 62 = 204 204 ÷ 2 = 102cm

DO: Ex 5.3 Pg 68 ALL BUT not: #1d iii; 2d 5a) X -7 -4 -1 3 i) 3 i) (5x + 4) + (4x + 3) -56 -29 -2 7 34 v) 9 + x + 7 9 12 15 16 19 vi) 9x + 7 DO: Ex 5.3 Pg 68 ALL BUT not: #1d iii; 2d

Exercise 5.3: answers 1a) i) 32; 39; 46 ii) Add 7 to the previous value iii) y = 7x – 3 b) i) 80; 75; 70 ii) Subtract 5 from the previous value iii) y = -5x + 105

Exercise 5.3: answers c) i) -1; 3; 7 ii) Add 4 to the previous value iii) y = 4x - 21 d) i) 160; 320; 640 ii) Multiply the previous value by 2

f) Do the opposite. ADD 1 and then DIVIDE by 2 2a) b) Multiply the input value by 2 and then subtract 1 c) y = 2x - 1 e) y = 2x – 1 y = 2(-4) - 1 y = -8 – 1 y = -9 x 1 2 3 4 5 10 17 46 102 y 7 9 19 33 91 203 f) Do the opposite. ADD 1 and then DIVIDE by 2 67 + 1 = 68 68 ÷ 2 = 34

Number of white tiles (y) 3a) 8 White tiles b) 13 White tiles c) 13 + 5 + 5 = 23 White tiles d) 8; 13; 18; 23 e) 28; 33; 38 f) y = 5x + 3 g) Pattern number (x) 1 2 3 4 5 Number of white tiles (y) 8 13 18 23 28 Number of blue tiles