For a polynomial function $p\left(x\right)$, what is its domain?

• A. Only $x\ge 0$
• B. Only integers $x$
• C. All real numbers except where the denominator is $0$
• D. All real numbers $(-\infty ,\infty )$

Answer: (D)

Verified step by step guidance

1. Recall that a polynomial function is an expression consisting of variables and coefficients combined using only addition, subtraction, multiplication, and non-negative integer exponents of variables.
2. Understand that polynomial functions do not have variables in the denominator or under even roots, which means there are no restrictions like division by zero or square roots of negative numbers.
3. Since there are no denominators or radicals that restrict the input values, the function is defined for every real number.
4. Therefore, the domain of any polynomial function is all real numbers, which can be expressed in interval notation as \((-\infty, \infty)\).
5. This means the polynomial function accepts any real number as input without any restrictions.