Exponential Function

The equation of an exponential function is:

Exponential Function

Given a positive real number a, the function that every real number x which corresponds to the power ax is called an exponential function.

Exponential Function

x y = 2x
-3 1/8
-2 1/4
-1 1/2
0 1
1 2
2 4
3 8

Graph of an Exponential Function

Exponential Function

x y = (1/2)x
-3 8
-2 4
-1 2
0 1
1 1/2
2 1/4
3 1/8

Exponential Function Graph

Properties of an Exponential Function

Domain : Any Real Number.

Range: R +.

It is continuous.

The points (0, 1) and (1, a) belong to the graph.

Increasing if a > 1.

Decreasing if a <1.

The curves y = ax and y = (1/a)x  are symmetrical about the y-axis .

Symmetrical Functions