$\"\"$

Definition :

The function defined by $\"\"$ is called as the natural exponential function.

It is denoted by $\"\"$ .

Properties of Natural exponential function :

The exponential function $\"\"$ is a continous function with domain $\"\"$ and range $\"\"$ .

Therefore $\"\"$ for all values of $\"\"$ .

Also

$\"\"$

The graph crosses the $\"\"$ axis at $\"\"$ .

When $\"\"$ the value increases,When $\"\"$ the graph decreases.

Domain of $\"\"$ is all real numbers and range is all positive real numbers(Never zero).

Graph $\"\"$ passes the vertical line test.

Graph $\"\"$ passes the horizantal line test-its inverse is also a function.

Graph $\"\"$ is asymptotic to the $\"\"$ -axis - gets very, very close to the $\"\"$ -axis but does not touch it or cross it.

$\"\"$ is continous, increasing, one-to-one and concave upwards on its entire domain.

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Properties of Natural exponential function is described.