This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to Question 3. Question 3 3.1.1 Consider the input numbers: 3, 5, 7, 9, 11. Rule: 2x. Step 1: Apply the rule 2x to each input number. For x=3: 2(3) = 6 For x=5: 2(5) = 10 For x=7: 2(7) = 14 For x=9: 2(9) = 18 For x=11: 2(11) = 22 The output numbers are 6, 10, 14, 18, 22. 3.1.2 Represent your answers using a flow diagram. c 3 \\ 5 \\ 7 \\ 9 \\ 11 Multiply by 2 c 6 \\ 10 \\ 14 \\ 18 \\ 22 3.2 Write down the rule for the following input and output values. Input values: 2, 4, 6, 8, 10 Output values: 3, 15, 35, 63, 99 Step 1: Analyze the relationship between input and output values. For input 2, output 3: 2^2 - 1 = 4 - 1 = 3 For input 4, output 15: 4^2 - 1 = 16 - 1 = 15 For input 6, output 35: 6^2 - 1 = 36 - 1 = 35 For input 8, output 63: 8^2 - 1 = 64 - 1 = 63 For input 10, output 99: 10^2 - 1 = 100 - 1 = 99 The rule is x^2 - 1. 3.3 What kind of outputs will be obtained by applying the rule -2x to all negative integers? Step 1: Consider examples of negative integers and apply the rule. If x = -1, output is -2(-1) = 2. If x = -2, output is -2(-2) = 4. If x = -3, output is -2(-3) = 6. The outputs will be positive even integers. 3.4 What kind of outputs will be obtained by applying the rule (x)/(5) to natural numbers smaller than 5? Step 1: Identify natural numbers smaller than 5. Natural numbers are positive integers (1, 2, 3, ...). So, natural numbers smaller than 5 are 1, 2, 3, 4. Step 2: Apply the rule (x)/(5) to each of these numbers. For x=1: (1)/(5) For x=2: (2)/(5) For x=3: (3)/(5) For x=4: (4)/(5) The outputs will be positive proper fractions. 3 done, 2 left today. You're making progress.