Graphs

• A function of the form f(x) = ka(x) is called an exponential function

• You need to be able to recognise and sketch the graphs of exponential functions

• The shape of an exponential graph depends on whether x is positive and negative

Exponential growth

• Exponential graphs appear in equations representing growth or decay

• If there are 500 bacteria in a Petri dish, and the number doubles every hour, then after h hours there will be N=500x2(h) bacteria in the Petri dish

• The graph of N against h will be an exponential graph

Finding missing values

• Some questions ask you to find the missing values in an exponential equation

• You can do this by substituting the values of x and y that you are given to get two equation and then work out k

Exponential graphs

• Exponential graphs are graphs in the form y=k(x)

• These graphs increase rapidly in the y direction and will never fall below the x-axis.

• An exponential graph will look like this:

How to identify an exponential graph:

• Graphs of Exponential Functions

  1. The graph passes through the point (0,1)

  2. The domain is all real numbers.

  3. The range is y>0.

  4. The graph is increasing.

  5. The graph is asymptotic to the x-axis as x approaches negative infinity.

  6. The graph increases without bound as x approaches positive infinity.

  7. The graph is continuous.