Question

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

Answer 1

Consider the exponential function `f(x)=a^(kx)`, where `a` and `k` are constant, `a, k in RR`.

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`.

https://www.desmos.com/calculator/g3k7pyi7dz