How can exponential functions be identified?

An exponential function is a function with a number that is positive and is not 0 or 1 that has x as its power. For example, f(x)=2^x
f(x)=2x-3 is not an exponential function, because there is no exponent.
f(x)=(89-120)*3/4x. Still not exponential.
f(x)=3.5^x. That is an exponential function.
Just remember that the number in the base cannot be negative because we would get the number i,  and it cannot be 0 or 1 because we would get 0 or 1 respectively. 
Hope that helped! :D. Comment if you have any questions.