A+ » VCE » Further Maths U3 & 4 Master Notes » OA4 Graphs and Relations » 1.6 Exponential Graphs

1.6 Exponential Graphs

Graphs of y=kxn

  • In Further Maths, we will analyse graphs of the form y=kx^{n}, where k is a constant known as the constant of proportionality, for the following values of n: -2, -1, 1, 2, 3. These forms are detailed individually below.

n= -2

  • The graph of y=kx^{-2} is symmetrical about the line x=0 and has two asymptotes. One at x=0, and one at y=0.
  • At x=0, the graph is undefined and on either side the graph curves upwards and goes towards infinity.
  • As you move away from the origin, the graph curves inwards and the value of y gets closer and closer to 0 the further you are from the origin.
  • All values of y are positive if k is positive, or negative if k is negative.

Example

The graph of y=3x^{-2} is shown below:

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