16Hit1600
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?

  1. A. 3hCorrect
  2. B. h
  3. C. 3h − 2
  4. 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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