Answer:
B
Explanation:
The differences in the terms of f(x) are + 3, + 5, + 7
Since the differences are not constant the relationship is not linear
Note the differences in the differences are + 2, + 2,
The second differences are constant indicating a quadratic relationship
Note the relationship between x and f(x)
x = 1 → 1² = 1 ← require to add 5, that is 1 + 5 = 6 ← value of f(x)
x = 2 → 2² = 4 ← require to add 5, that is 4 + 5 = 9 ← value of f(x)
x = 3 → 3² = 9 ← require to add 5, that is 9 + 5 = 14 ← value of f(x)
x = 4 → 4² = 16 ← require to add 5, that is 16 + 5 = 21 ← value of f(x)
Thus f(x) = x² + 5 → B