Question

Which of the following are decreasing functions?

Select all that apply

f(x) = 2^x

f(x) = –3^x

f(x) = 0.5^x

f(x) = 1^x

Answer 1

Exponential functions a^x are
- increasing if a > 1,
- decreasing if 0 < a < 1,
- constant if a = 1.

Interpret −3^x as −(3^x). Then:
- 2^x: a = 2 > 1 → increasing (not decreasing).
- −3^x = −(3^x): derivative = −(ln 3)3^x < 0 → decreasing.
- 0.5^x: a = 1/2 (0 < a < 1) → decreasing.
- 1^x: constant = 1 → neither increasing nor decreasing.

Therefore the decreasing functions are: −3^x and 0.5^x.