This topic examines the graphs of functions of the type y = x a, where a is a constant.
Revision of the rules of exponents, also called powers may be useful and are covered in Year 12, Topic 3
Some power functions, such as y = x2 and y = x3 and y = 1 / x = x -1 have been well covered in previous years.
Because many of these graphs have few intercepts and features the best method is to learn the basic types for different values of a and then plot a few points to get the shape.
The table below shows examples of power functions for different values of a.
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a is a positive integer
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a = 2
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a = 3
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a = 4
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a is a negative integer
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a = − 1
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a = − 2
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a = − 4
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a is not an integer
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a < 0 a = − 0.9 |
0 ≤ a ≤ 1 a = 0.5 |
a > 1 a = 1.8 |
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Notes for the power function y = xa
- If a is a whole number then x can have any value.
- If a is a negative integer then x can have any value except 0.
- If a is a any other type of number then x almost always has to be positive.
These properties are all illustrated on the graphs in the table above.
