In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. h(x)=7x^3+2x^2+1/x

A polynomial function is a mathematical expression that involves variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer. Functions that include variables in the denominator or have negative exponents are not considered polynomial functions.

The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in the polynomial 4x^5 + 3x^2 - 2, the degree is 5. The degree provides important information about the behavior of the polynomial function, including the number of roots and the end behavior of the graph.

To determine if a function is a polynomial, it is essential to identify any non-polynomial terms. For instance, terms that involve division by a variable (like 1/x) or negative exponents (like x^-1) disqualify the function from being a polynomial. Recognizing these terms is crucial for accurately classifying functions and determining their properties.