The exponential functions are ,
,
and
.
Graph the functions ,
,
and
on a common screen.
From the properties of the exponential functions,
\If , then
is decreasing.
If , then
is increasing.
Observe the graph,
\Therefore, the functions and
, which are having base greater than one are monotonoically increasing.
The above curves are approaching zero as and the curves are approaching infinite as
.
Therefore, the functions and
are monotonoically decreasing.
The above curves are approaching zero as and the curves are approaching infinite as
.
All the curves passing through the point .
Graph:
\The functions and
are monotonoically increasing.
The functions and
are monotonoically decreasing.