As the base a of an exponential function fxax where a 1 incr

As the base a of an exponential function f(x)=a^x, where a> 1, increases, what happens to the behavior of its graph for x > 0? What happens to the behavior of its graph for x< 0? Please write your answers in words and using symbol notations.

Solution

f(x) = a^x for a >1

for x <0; f(x) = a^-x = 1/a^x

So, x becomes more negative f(x) becomes less and less.

x<<0 ; f(x) ---> 0

for x>0 ; f(x) = a^x

x>>0 ; f(x) increases more and more

x>>0 ; f(x) -----> infinity