Exponential Function
The equation of an exponential function is:
Given a positive real number a, the function that every real number x which corresponds to the power ax is called an exponential function.
| x | y = 2x |
|---|---|
| -3 | 1/8 |
| -2 | 1/4 |
| -1 | 1/2 |
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| x | y = (1/2)x |
|---|---|
| -3 | 8 |
| -2 | 4 |
| -1 | 2 |
| 0 | 1 |
| 1 | 1/2 |
| 2 | 1/4 |
| 3 | 1/8 |
Properties of an Exponential Function
Domain : 
.
Range: 
.
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 .
