Let's solve each of the two-step function machines step by step. Each machine takes an
input, applies two operations in sequence (e.g., multiply, then add), and produces an
output.
We’ll go through
Question 1 and
Question 2 one by one.
---
✔ Question 1
#### a)
Input:
5
→ ×3 → 5 × 3 =
15
→ +2 → 15 + 2 =
17
✔ Output: 17
#### b)
Input:
3
→ ×3 → 3 × 3 =
9
→ +4 → 9 + 4 =
13
✔ Output: 13
#### c)
Input:
10
→ ×3 → 10 × 3 =
30
→ -2 → 30 - 2 =
28
✔ Output: 28
#### d)
Input:
7
→ ×4 → 7 × 4 =
28
→ -2 → 28 - 2 =
26
✔ Output: 26
#### e)
Input:
5
→ +2 → 5 + 2 =
7
→ ×2 → 7 × 2 =
14
✔ Output: 14
#### f)
Input:
6
→ +2 → 6 + 2 =
8
→ ×3 → 8 × 3 =
24
✔ Output: 24
#### g)
Input:
10
→ +3 → 10 + 3 =
13
→ ×2 → 13 × 2 =
26
✔ Output: 26
#### h)
Input:
8
→ +3 → 8 + 3 =
11
→ ×3 → 11 × 3 =
33
✔ Output: 33
---
✔ Question 2
#### a)
Input:
2
→ ×4 → 2 × 4 =
8
→ +6 → 8 + 6 =
14
✔ Output: 14
#### b)
Input:
3
→ ×3 → 3 × 3 =
9
→ +7 → 9 + 7 =
16
✔ Output: 16
#### c)
Input:
5
→ ×4 → 5 × 4 =
20
→ -2 → 20 - 2 =
18
✔ Output: 18
#### d)
Input:
9
→ ×2 → 9 × 2 =
18
→ +8 → 18 + 8 =
26
✔ Output: 26
#### e)
Input:
5
→ +2 → 5 + 2 =
7
→ ×7 → 7 × 7 =
49
✔ Output: 49
#### f)
Input:
7
→ -1 → 7 - 1 =
6
→ ×2 → 6 × 2 =
12
✔ Output: 12
#### g)
Input:
10
→ -1 → 10 - 1 =
9
→ ×3 → 9 × 3 =
27
✔ Output: 27
#### h)
Input:
12
→ -2 → 12 - 2 =
10
→ ×3 → 10 × 3 =
30
✔ Output: 30
---
📌 Summary of Answers
####
Question 1
a) 17
b) 13
c) 28
d) 26
e) 14
f) 24
g) 26
h) 33
####
Question 2
a) 14
b) 16
c) 18
d) 26
e) 49
f) 12
g) 27
h) 30
---
🔍 Explanation:
Each function machine follows
two steps:
1. Apply the first operation to the input.
2. Use the result from step 1 as the input for the second operation.
Always
do operations in order — left to right.
For example:
If input is 5, and the steps are
×3 → +2:
- First: 5 × 3 = 15
- Then: 15 + 2 = 17
This is equivalent to the algebraic expression:
(input × 3) + 2
You can write a general rule for any such machine.
Let me know if you'd like the algebraic expressions for each!
Parent Tip: Review the logic above to help your child master the concept of function machine worksheet.
