# What characteristics are identified from the graph of an exponential function?

Consider the exponential function $f \left(x\right) = {a}^{k x}$, where $a$ and $k$ are constant, $a , k \in \mathbb{R}$.
I prepared a dynamic plot that can be used to study the properties of the exponential function as $a$ and $k$ take various values.
Please use the provided sliders to change the values of the parameters $a$ and $k$ and see what happens to the graph of the function.
Pay particular attention to the cases when $0 < a < 1$ and $a > 1$. For each of these cases, see what happens when $k < 0$ and $k > 0$.