Question

For every value of \( x \), the function \( f(x) = \frac{1}{a^x}, a>0 \) is

• A. decreasing
• B. increasing
• C. Constant
• D. Neither increasing nor decreasing

Hint:

Exponential functions of the form \( f(x) = \frac{1}{a^x} \), where \( a>1 \), are always decreasing functions.

Answer 1

The Correct Option is A

Step 1: Understand the behavior of the function.
The function \( f(x) = \frac{1}{a^x} \) is an exponential function with base \( a \), where \( a>0 \). Since the base \( a \) is greater than 1, this function is decreasing as \( x \) increases. The rate of decrease becomes slower as \( x \) increases.

Step 2: Conclusion.
Thus, the function is decreasing, corresponding to option (A).