Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.4 Evaluation Logarithms and the Change-of-Base Theorem - 4.4 Exercises - Page 456: 1

The function is increasing over its entire domain.

If we differentiate the function, we get $a^x$$\ln a$ as a >1 so $\ln a$ is > 0 and $a^x$ is > 0 as well. Hence the derivative is positive throughout the domain. Hence the function is increasing throughout the domain.