Let's solve each of the four “double function machines” step by step. Each machine applies
two operations in sequence to the input to produce the output.
---
## 🔴 Machine 1: ×2 → +5
This means:
Output = (Input × 2) + 5
Given:
- Input = 3 → Output = (3 × 2) + 5 = 6 + 5 =
11
- Input = 4 → Output = (4 × 2) + 5 = 8 + 5 =
13
- Output = 19 → Solve for Input:
Let input be `x` → (x × 2) + 5 = 19 → 2x = 14 → x =
7
- Output = 21 → (x × 2) + 5 = 21 → 2x = 16 → x =
8
✔ Completed Table:
| Input | Output |
|-------|--------|
| 3 | 11 |
| 4 | 13 |
| 7 | 19 |
| 8 | 21 |
---
## 🟢 Machine 2: +2 → ×3
This means:
Output = (Input + 2) × 3
Given:
- Input = 4 → Output = (4 + 2) × 3 = 6 × 3 =
18
- Input = 5 → Output = (5 + 2) × 3 = 7 × 3 =
21
- Output = 24 → Solve for Input:
(x + 2) × 3 = 24 → x + 2 = 8 → x =
6
- Output = 33 → (x + 2) × 3 = 33 → x + 2 = 11 → x =
9
✔ Completed Table:
| Input | Output |
|-------|--------|
| 4 | 18 |
| 5 | 21 |
| 6 | 24 |
| 9 | 33 |
---
## 🟡 Machine 3: ÷3 → +4
This means:
Output = (Input ÷ 3) + 4
Given:
- Input = 6 → Output = (6 ÷ 3) + 4 = 2 + 4 =
6
- Input = 9 → Output = (9 ÷ 3) + 4 = 3 + 4 =
7
- Output = 11 → Solve for Input:
(x ÷ 3) + 4 = 11 → x ÷ 3 = 7 → x =
21
- Output = 14 → (x ÷ 3) + 4 = 14 → x ÷ 3 = 10 → x =
30
✔ Completed Table:
| Input | Output |
|-------|--------|
| 6 | 6 |
| 9 | 7 |
| 21 | 11 |
| 30 | 14 |
---
## 🔵 Machine 4: –4 → ÷3
This means:
Output = (Input – 4) ÷ 3
Given:
- Input = 16 → Output = (16 – 4) ÷ 3 = 12 ÷ 3 =
4
- Input = 22 → Output = (22 – 4) ÷ 3 = 18 ÷ 3 =
6
- Output = 9 → Solve for Input:
(x – 4) ÷ 3 = 9 → x – 4 = 27 → x =
31
- Output = 12 → (x – 4) ÷ 3 = 12 → x – 4 = 36 → x =
40
✔ Completed Table:
| Input | Output |
|-------|--------|
| 16 | 4 |
| 22 | 6 |
| 31 | 9 |
| 40 | 12 |
---
##
✔ Final Answer Summary:
Machine 1 (×2 → +5)
| Input | Output |
|-------|--------|
| 3 | 11 |
| 4 | 13 |
| 7 | 19 |
| 8 | 21 |
Machine 2 (+2 → ×3)
| Input | Output |
|-------|--------|
| 4 | 18 |
| 5 | 21 |
| 6 | 24 |
| 9 | 33 |
Machine 3 (÷3 → +4)
| Input | Output |
|-------|--------|
| 6 | 6 |
| 9 | 7 |
| 21 | 11 |
| 30 | 14 |
Machine 4 (–4 → ÷3)
| Input | Output |
|-------|--------|
| 16 | 4 |
| 22 | 6 |
| 31 | 9 |
| 40 | 12 |
All tables are now complete! 🎉
Parent Tip: Review the logic above to help your child master the concept of function machines worksheet.
