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Advanced MathMediumIdentifying a function that is decreasing everywhere

Advanced Math practice question

Which of the following functions is decreasing for all real values of x?

  1. A. f(x) = 5(0.9)ˣCorrect
  2. B. f(x) = 5(1.1)ˣ
  3. C. f(x) = x²
  4. D. f(x) = −(0.5)ˣ

Answer: A. f(x) = 5(0.9)ˣ

A base between 0 and 1 with a positive coefficient decays as x increases. The others rise, at least somewhere.

Why the other answers are wrong

B. f(x) = 5(1.1)ˣ
Base 1.1 grows.
C. f(x) = x²
x² decreases for x < 0 but increases for x > 0.
D. f(x) = −(0.5)ˣ
−(0.5)ˣ rises toward 0 as x increases (its values are −1, −0.5, −0.25, and so on).

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