Question

What is the domain of a polynomial?

Short answer

Answer: The domain of a polynomial function is the set of all real numbers, which can be represented in mathematical notation as (-∞, +∞).

Step-by-step solution

Definition of a polynomial

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents combined using addition, subtraction, and multiplication. A polynomial function can be represented as: P(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0 where a_n, a_(n-1), .. a_1, and a_0 are the coefficients, n is the highest exponent, and x is the variable.

Domain Considerations

When determining the domain of a function, we need to consider if there are any restrictions on the input value x. For instance, if there was a square root or a fraction with a variable in the denominator, we would need to do some analysis to figure out which values of x are valid inputs. However, for polynomial functions, there are no restrictions on the input value x. Since we can multiply, add, and subtract any numbers (including negative numbers), the input x can be any real number.

The Domain of a Polynomial

From our domain considerations, we can conclude that the domain of a polynomial is the set of all real numbers. In mathematical notation, this can be written as: Domain(P(x)) = (-∞, +∞) The domain of a polynomial is thus all real numbers because there are no restrictions on the input value x.