Determine which functions are polynomial functions. For...

Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, state why not. Write each polynomial in standard form. Then identify the leading term and the constant term.
$$
h(x)=3-\frac{1}{2} x
$$

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Key Concepts

Polynomial Function

A polynomial function is an algebraic expression formed by summing a finite number of terms, each a product of a constant and a nonnegative integer power of a variable. It is typically written as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable present in the polynomial when it is expressed in its standard form. This degree indicates the maximum number of roots and the general shape of the graph.

Standard Form

Writing a polynomial in standard form involves arranging its terms in descending order of degree, from the highest power to the lowest. This format simplifies the analysis of the polynomial’s properties, such as its degree and leading coefficient.

Leading Term

The leading term of a polynomial is the term with the highest degree in its standard form. Its coefficient, known as the leading coefficient, is crucial in determining the end behavior of the polynomial function.

Constant Term

The constant term is the term in a polynomial that does not include the variable. It represents the value of the function when the variable is set to zero and is an essential part of the polynomial's overall structure.

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