When graphing a function with exponentials in the numerator and denominator if you know its defined for all $x$ in $R$, can you do anything more than check the limits as it approaches positive and negative infinity and then check a point like x=0 and then just give it a go at graphing it?
Thanks
You are over simplifying the problem of graphs involving exponential functions.
May be your method works for some simple functions like logistic equations but it can get more complicated than just checking the end behavior and the intercepts.