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
• As x gets smaller, y gets smaller and closer to the x-axis.
• 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
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.
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.