AlgebraHardDifference of outputs from a difference of inputs
Algebra practice question
For a linear function f, f(4) − f(1) = 18. What is the value of f(9) − f(2)?
- A. 42Correct
- B. 18
- C. 36
- D. 54
Answer: A. 42
f(4) − f(1) spans 3 units of x, so the slope is 18 ÷ 3 = 6. Then f(9) − f(2) spans 7 units: 7 · 6 = 42.
Why the other answers are wrong
- B. 18
- The two differences span different x-distances (3 and 7), so they cannot be equal.
- C. 36
- 36 is 6 · 6 — the span from x = 2 to x = 9 is 7, not 6.
- D. 54
- 54 is 18 · 3; the correct scaling is by 7/3, giving 42.
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