AlgebraVery hardDefining a linear function from a constant change
Algebra practice question
The function g is linear, and g(x) − g(x − 1) = −4 for every value of x. If g(3) = 2, which of the following defines g?
- A. g(x) = −4x + 14Correct
- B. g(x) = −4x + 2
- C. g(x) = 4x − 10
- D. g(x) = −4x − 14
Answer: A. g(x) = −4x + 14
The slope is −4, and g(3) = 2 gives 2 = −12 + b, so b = 14.
Why the other answers are wrong
- B. g(x) = −4x + 2
- This gives g(3) = −10.
- C. g(x) = 4x − 10
- The slope is +4, so g increases by 4 each step.
- D. g(x) = −4x − 14
- This gives g(3) = −26.
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