is continuous, always increasing and for all values of .

For the continuous function, there must be no breaks, holes or gaps in the graph.

For the increasing function, the -value increases as the -value increases.

For for all values of , the graph must be above the -axis. In other words the range of the function is all positive real numbers.

An exponential function is perfect model of a function where for all values of .

Graph:

Observe the graph:

tends to go up as it goes along and for all values of .

Graph:

.