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# 1.6 Exponential Graphs

Contents

### 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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