Advanced MathMediumChange in a linear function's output for a change in input
Advanced Math practice question
The function f is defined by f(x) = 3x − 2. Which expression is equal to f(x + h) − f(x) for all x and h?
- A. 3hCorrect
- B. h
- C. 3h − 2
- D. 3x + 3h
Answer: A. 3h
f(x + h) = 3x + 3h − 2. Subtracting f(x) = 3x − 2 leaves 3h.
Why the other answers are wrong
- B. h
- h forgets the factor 3.
- C. 3h − 2
- 3h − 2 fails to cancel the −2 terms.
- D. 3x + 3h
- 3x + 3h is f(x + h) + 2, not the difference.
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