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Two-Step Function Machines

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Two-Step Function Machines

Two-step function machine diagram

🔧 Part 1: Following Two-Step Rules

1. Use the function machine: Input → multiply by 3 → add 5 → Output

Complete the table:

Input 2: 2 × 3 = _____, then _____ + 5 = _____

Input 4: 4 × 3 = _____, then _____ + 5 = _____

Input 7: 7 × 3 = _____, then _____ + 5 = _____

2. Function machine: Input → subtract 3 → multiply by 4 → Output

Find the outputs:

Input 8: _________ → _________

Input 5: _________ → _________

Input 10: _________ → _________

3. Which algebraic expression matches this rule: "multiply by 2, then add 7"?

x + 7 × 2

2x + 7

7x + 2

2 + 7x

4. What is the output when x = 6 in the expression 3x - 4?

14

18

22

10

🔍 Part 2: Function Machine Detective

5. Find the missing operation:

Input 5 → multiply by 3 → _______ → Output 11

6. Complete this function machine:

Input 4 → _______ → add 6 → Output 20

7. Work backwards! If the output is 23 and the rule is "multiply by 4, then subtract 1", what was the input?

Working: _________________________

Input: _________

8. Write the algebraic expression for each function machine:

a) Add 8, then multiply by 2: ___________

b) Multiply by 5, then subtract 3: ___________

c) Subtract 4, then multiply by 3: ___________

💭 Part 3: Problem Solving

9. Sarah's function machine uses the rule 2x + 5. If she puts in the number 7, what comes out?
10. Explain why the order of operations matters in two-step function machines. Use an example to support your answer.

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