AlgebraVery hardLinear function from a functional relation
Algebra practice question
A linear function f satisfies f(x + 2) = f(x) + 6 for all values of x, and f(1) = 4. What is the value of f(−3)?
Answer: -8
A rise of 6 over a step of 2 means the slope is 3, so f(x) = 3x + 1 and f(−3) = −8.
Common wrong answers
- If you answered 8
- 8 has the sign wrong.
- If you answered -2
- −2 uses f(−3) = f(1) − 6, stepping back only once.
- If you answered -20
- −20 uses a slope of 6.
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