Question

How can you determine if a function is exponential or not without graphing?

Answer 1

If 'b' is greater than 1, then it is exponential growth, but if 'b' is smaller than 1, then it is an exponential decay.

You just need to remember this formula, and that's it.
Good luck with that.

Answer 2

Keep in mind that we also need to know that the graph is, in fact, an exponential function. Not every graph that looks exponential really is exponential. We need to know the graph is based on a model that shows the same percent growth with each unit increase in x, which in many real world cases involves time.