In general: For an exponential function whose exponent tends to #+- oo# as #x->oo#, the function tends to #oo# or 0 respectively as #x->oo#.

Note that this applies similarly for #x->-oo# Further, as the exponent approaches #+-oo#, minute changes in #x# will (typically) lead to drastic changes in the value of the function.

Note that behavior changes for functions where the base of the exponential function, i.e. the #a# in #f(x) = a^x#, is such that #-1<=a<=1#.

Those involving #-1<=a<0# will behave oddly (as the #f(x)# will not take on any real values, save where #x# is an integer), while #0^x# is always 0 and #1^x# is always 1.

For those values #0<a<1#, however, the behavior is the opposite of the long-term behavior noted above.

For functions #a^x# with #0<a<1#, as #x->oo#, #f(x) ->0#, and as #x->-oo#, #f(x) ->oo#