AlgebraMediumIdentifying a linear function from a table
Algebra practice question
x: 1, 2, 3
f(x): 9, 14, 19
The table gives three values of a linear function f. Which equation defines f?
- A. f(x) = 5x + 4Correct
- B. f(x) = 4x + 5
- C. f(x) = 5x − 4
- D. f(x) = 9x
Answer: A. f(x) = 5x + 4
From x = 1 to x = 2, f rises by 5, so the slope is 5. Then f(1) = 9 gives 9 = 5 + b, b = 4: f(x) = 5x + 4. Check x = 3: 19 ✓.
Why the other answers are wrong
- B. f(x) = 4x + 5
- 4x + 5 gives 9 at x = 1 but 13 at x = 2, not 14.
- C. f(x) = 5x − 4
- 5x − 4 has the right slope but gives 1 at x = 1.
- D. f(x) = 9x
- 9x fits only the first row (18 at x = 2, not 14).
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