Classification – Ordered pairs (function rule): identify the odd one out. In three pairs, the second term equals first^3 + 1; one pair violates this mapping. Which pair is different? Options: 1 : 2, 3 : 28, 4 : 65, 2 : 7.

Introduction / Context:
Number-pair classifications often apply a fixed function from the first to the second component. Spotting the rule exposes the misfit pair.

Given Data / Assumptions:

• Candidate rule: y = x^3 + 1.
• Pairs: (1,2), (3,28), (4,65), (2,7).

Concept / Approach:
Evaluate y − 1 and compare with x^3 for each pair.

Step-by-Step Solution:
x=1 → x^3+1=1+1=2 → matches 2.x=3 → 27+1=28 → matches 28.x=4 → 64+1=65 → matches 65.x=2 → 8+1=9 ≠ 7 → violation.

Verification / Alternative check:
Compute backward: for y=7, y−1=6; cube root of 6 is non-integer, confirming mismatch.

Why Other Options Are Wrong:
1:2, 3:28, 4:65: Each satisfies y = x^3 + 1 and belongs together.

Common Pitfalls:
Trying linear rules (e.g., y=2x+1) which do not fit all three compliant pairs.

Final Answer:
2 : 7