Why does the exponential-function domain need greater than zero and unequal to one?

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For example, f(x) = 0ˣ. Is it a exponent? Is it a function? I think f(x) = 0ˣ is an exponential function, but it's base is zero. Do you think? Can you help me?

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Maybe I knowed after I saw this document(http://jwilson.coe.uga.edu/EMAT6500/ClassSit/Major/Exponential%20Bases.pdf). Thanks a lot.