What is the end behavior of the function #f(x) = 5^x#?
The graph of an exponential function with a base > 1 should indicate "growth". That means it is increasing on the entire domain. See graph:
For an increasing function like this, the end behavior at the right "end" is going to infinity. Written like: as
That means that large powers of 5 will continue to grow larger and head toward infinity. For example,
The left end of the graph appears to be resting on the x-axis, doesn't it? If you calculate a few negative powers of 5, you will see that they get very small (but positive), very quickly. For example: