In high school, we learned the definition and properties of exponential functions as commonly used basic elementary functions, and then summarized them as follows.

　　1. Definition and properties of exponential function

( is a constant, and , ) ,

Its domain is all real numbers .

　　When , the exponential function increases monotonically;

　　When , the exponential function decreases monotonically .

　　The graph of and is symmetrical about axis (as shown below) . The most commonly used one is the exponential function with as the base

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【 Animation 】

　　2. Properties and operations of exponential functions

　　(1)  The influence of the base on the value of the exponential function;

　　(2)  Use the properties of exponential functions to compare sizes;

　　(3) Arithmetic rules for rational number exponents .