13.1 Exponential Functions

  • The Exponential Function • Graphing Exponential Functions • Features of Exponential Functions

In Chapter 11, we showed that any rational number can be used as an exponent. Now letting the exponent be a variable, we define the exponential function as

y = bx (13.1)

where b > 0 , b ≠ 1 ,  and x is any real number. The number b is called the base.

For an exponential function, we use only real numbers. Therefore, b > 0 ,  because if b were negative and x were a fractional exponent with an even-number denominator, y would be imaginary. Also, b ≠ 1 ,  since 1 to any real power is 1 (y would be constant).

EXAMPLE 1 Exponential functions

From the definition, y = 3x is an exponential function, but y = ( − 3)x is not because ...

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