Exponential Functions

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

Exponential Function

Examples

Exponential Function

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

Exponential Function Graph

Exponential Function

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

Exponential Function Graph

Properties

Domain: Any Real Number.

Range: Any Real Number.

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 .

Graph of Symmetrical Exponential Functions


Exponential Functions Worksheet