2009

11.02

11.02

The function defined by where , and the exponent is any real number, is called an **exponential function** with base

When you work with exponential functions, it may be necessary to apply **rules for exponents**. These rules are as follows, where and are real numbers and and are positive.

Graphs of some exponential functions are shown below:

Here, some **properties** of exponential functions

- The
**domain**of an exponential function is all real numbers - The
**range**is all positive real numbers - Since for every base , each graph has y-intercept (0, 1). There is no x-intercept.
- If , then is an increasing function; its graph rises from left to right. Also

and

- Thus as , the graph has the x-axis as a horizontal asymptote.
- If , then is a decreasing function; its graph falls from left to right. Also

and

- Thus as , the graph has the x-axis as the horizontal asymptote.

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