AlgebraHardLinear function from a functional relationship
Algebra practice question
A linear function f satisfies f(x + 4) = f(x) + 10 for every value of x, and f(2) = 7. What is the value of f(10)?
Answer: 27
Every 4 units of x add 10 to f, so the slope is 10/4 = 2.5. From x = 2 to x = 10 is 8 units: f(10) = 7 + 2(10) = 27.
Common wrong answers
- If you answered 17
- 17 is f(6), one step of 4.
- If you answered 32
- 32 comes from 7 + 2.5 × 10, using x = 10 as the number of steps instead of the distance from x = 2.
- If you answered 37
- 37 adds 10 three times, as if 10 were the change per 4 units from x = 2 to 14.
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