AlgebraEasy–MediumFunction from a table
Algebra practice question
x | f(x)
0 | 4
3 | −2
Which equation defines the linear function f?
- A. f(x) = −2x + 4Correct
- B. f(x) = 2x + 4
- C. f(x) = −2x − 2
- D. f(x) = 4x − 2
Answer: A. f(x) = −2x + 4
From x = 0 to x = 3, f falls from 4 to −2: slope (−2 − 4)/3 = −2. f(0) = 4 is the y-intercept. So f(x) = −2x + 4. Check: f(3) = −6 + 4 = −2.
Why the other answers are wrong
- B. f(x) = 2x + 4
- A slope of +2 would make f rise; the table shows f falling as x increases.
- C. f(x) = −2x − 2
- −2 is f(3), not the intercept. The intercept is f(0) = 4.
- D. f(x) = 4x − 2
- 4x − 2 gives f(0) = −2, but the table says f(0) = 4.
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