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I determine the difference between a increasing function, decreasing function , and undefined function because these are the rules of function.

f(x) is a increasing function
0<b<1, f(x) is a decreasing function
f(x) is a undefined function

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The domain of the function is "infinite domain" Same for the range too "infinite range"

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How do you determine if an exponential function is increasing or decreasing?

If b>1, f(x) is an increasing function. If 0<b<1, f(x) is a decreasing function. If b≤0, f(x) is not defined.

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An exponent is not a function but you can make it a function if you give it a form such as an input to figure out the output

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I believe a fractional exponent is a skill of showing exponents and roots in a variety of ways.

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for exmaple If b>1, f(x) is an increasing function. If 0<b<1, f(x) is a decreasing function. If b≤0, f(x) is not defined.

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the domain of the function is (-∞,∞) the range of the function is (0, ∞)

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The Domain of the function is (-∞,∞) the range of the function is ( 0,∞)

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Domain:(-∞,∞)
range :(2,∞)

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Exponential functions have the form f(x) = b x, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.

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To form an exponential function, we let the independent variable be the exponent.

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I would explain Fractional Exponents as a way to use powers and different roots in Math .

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A fractional exponent is a technique for expressing powers and roots together.     EX:1612 is another way of writing √16; 813 is another way of writing 3√8.