1. FUNCTIONS & RELATIONSHIPS 1
Chapter 5, Page 62

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

3. 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 =
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

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

5. 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

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

7. 2a) i) y = 3x – 5 y = 3(-3) – 5 y = 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 =
y = -8
b) iv) y = 3x - 5
y = 3(0) - 5
y = 0 – 5
y = - 5

8. 2a) v) y = 3x – 5 y = 3(1) – 5 y = 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

9. 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

10. 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

11. 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 =
y = 17 11
-19
-51
-107
7- 2n

12. 2a)
b) Subtract 3 from the output number; then divide by two to get the input number.
c) y = 2x + 3

13. 3b) y = 4x – 3 3c) y = 3x - 5 Input (x) 5 6 7 8 9 Output (y) 17 21 2529 33
Input (x) 5 6 7 8 9
Output (y) 10 13 16 19 22

14. 4a) P = l + b + l + b = 34 + 19 + 34 + 19 = 106cm P = 2l + 2b = 2(34) + 2(19) = 68 + 28
= 2 ( )
= 2(53)
= 106cm
4b) 328 – 62 – 62
= 204
204 ÷ 2 = 102cm

15. 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

16. 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

17. 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

18. 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
= 68
68 ÷ 2 = 34

19. Number of white tiles (y)
3a) 8 White tiles b) 13 White tiles c) = 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