Advanced MathMediumIdentifying a function type from second differences
Advanced Math practice question
The points (0, 5), (1, 8), (2, 13), and (3, 20) all lie on the graph of a function f. Which type of function could f be?
- A. A quadratic functionCorrect
- B. A linear function
- C. An exponential function
- D. A constant function
Answer: A. A quadratic function
The outputs rise by 3, 5, and 7: the first differences are not constant (so not linear), but the second differences are all 2, which is the mark of a quadratic. (f(x) = x² + 2x + 5 fits.)
Why the other answers are wrong
- B. A linear function
- A linear function has constant first differences; here they grow.
- C. An exponential function
- An exponential function has a constant ratio; 8/5, 13/8, and 20/13 are not equal.
- D. A constant function
- The outputs change.
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