A function of the form y = a^{x} is called an exponential function.
a is the base and x is the exponent. Exponential functions are sometimes known as growth or decay curves.
A spreadsheet can be used to investigate this type of function.
e.g. For the function y = 2^{x}
Note
• As x gets smaller, y gets smaller and closer to the xaxis. • As x gets larger, y gets larger. • This is the shape of the graph of an exponential function. • Functions of the type 
Transformations of Exponential Graphs
Example 1
y = 2^{x} This is a basic exponential function. y = 2^{x} (is same as y = 0.5^{x}) The (x) exponent makes a reflection in the yaxis. y = 2^{x} The negative sign makes each value negative and gives a reflection in the xaxis.


Example 2
y = 10^{x} The bigger the base number the steeper the graph. y = 10^{x2} The graph is moved 2 units forward. y = 10^{x} − 2 The graph is moved down 2 units. 
Graph of y = e^{x}
y = e^{x} is a special exponential function.
The value of e is 2.718281 (to 7 sig.fig.).
It is special because at any point on the graph the gradient of the curve is equal to the yvalue at that point.
The gradient of the graph at the point (0, 1) is 1.
The gradient of the graph at the point (1, 2) is 2, etc, etc.