VectorMen.jpgA function of the form y = ax 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 = 2x

Y11_Exponential_Functions_01.gif Note

• As x gets smaller, y gets smaller and closer to the x-axis.
The x-axis is an asymptote.

• As x gets larger, y gets larger.

• This is the shape of the graph of an exponential function.

• Functions of the type
y = ax always pass through the point (0, 1).



Transformations of Exponential Graphs

Example 1


y = 2x

This is a basic exponential function.

y = 2-x (is same as y = 0.5x)

The (-x) exponent makes a reflection in the y-axis.

y = -2x

The negative sign makes each value negative and gives a reflection in the x-axis.



Example 2


y = 10x

The bigger the base number the steeper the graph.

y = 10x-2

The graph is moved 2 units forward.

y = 10x − 2

The graph is moved down 2 units.


Graph of y = ex

y = ex 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 y-value 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.