Q:

# What Are Exponential Function Rules?

A:

Exponential function rules are the mathematical guidelines for functions that take the form of f(x) = b^x, where the base is a positive real number. With these functions, the growth rate is proportional to their value.

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While there are many rules that govern exponential functions, there are several main rules used to dictate specific functions. One unique exponential function is e^x, where the growth rate of this function at x is exactly e^x. Another unique relationship occurs when any exponential function takes the form b^0. This function is always equal to one, provided that the value of b is not equal to zero.

Other rules are more general. For exponential functions that take the form b^x+y, their value is equal to (b^x)(b^y). For functions of the form b^xy, their value is equal to (b^x)^y. Similar to this rule, functions that take the form ba^x are equal to (b^x)(a^x). Additionally, functions that take the form b^-x are equal to 1/(b^x).

It should also be noted that square root functions are a special type of exponential function. These functions of the form f(x) = sqrt(x) are equal to x^1/2. The same can be said for cubic root and other functions that take a similar form.