Understanding the Domain of Polynomial Functions | Explained with Examples

Domain of a polynomial function

The domain of a polynomial function is the set of all real numbers for which the function is defined

The domain of a polynomial function is the set of all real numbers for which the function is defined. In other words, it is the set of x-values that can be inputted into the polynomial function, yielding a valid output.

For polynomial functions, the domain is typically all real numbers, unless there are specific restrictions given by the problem.

Consider the general form of a polynomial function: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + … + a_1*x + a_0, where a_n, a_(n-1), …, a_0 are constants, and n is a non-negative integer.

Since polynomial functions are defined for all real numbers, the domain of a polynomial function is (-∞, ∞), which means that any real number can be a valid input for the function.

However, there might be some particular cases where restrictions on the domain exist. For example, if the function has a fractional exponent or a square root within it, then the domain might be limited to only those values of x for which the exponent or the radicand is defined.

Therefore, when determining the domain of a polynomial function, you should always check if there are any explicit limitations specified in the problem or if there are any operations within the function that restrict the domain.

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