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?
- A. f(x) = 5(0.9)ˣCorrect
- B. f(x) = 5(1.1)ˣ
- C. f(x) = x²
- 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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