Power Exponential and Logarithmic Functions

When a number a is multiplied by itself n times, we write a". where n is called the exponent. This leads to the rules of exponents:

Intuitively, we may think of n as an integer, but in fact n could be any real number. The power function takes the form y = ax". x e R. a > 0

(Note that the rectangular hyperbola is a special form of the power function with b = — I. The linear function is also a special case with b — I. The quadratic may be thought of as the sum of two power functions. )

Figure 2.26 shows two power functions for x e R+ where/; > I and b < — 1.

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