Understanding Polynomial Functions

The video tutorial explains how to identify polynomial functions by examining their terms. It defines polynomial functions as sums or differences of monomials, where each term is a real number, a variable, or a product of a real number and variables with non-negative integer exponents. Through examples, the tutorial demonstrates how to verify if a function is polynomial or not by analyzing the exponents of the variables. Functions f(x) and g(x) are confirmed as polynomial functions, while h(x) and j(x) are not due to non-integer and negative exponents, respectively.

What is a key characteristic of a polynomial function?

• It can have fractional exponents.

• It must include at least one constant term.

• It is a sum or difference of monomials with non-negative integer exponents.

• It includes terms with negative exponents.

Why is f(x) = -8x^3 + 4 considered a polynomial function?

• It has a negative coefficient.

• It is a sum of two monomials with non-negative integer exponents.

• It includes a division by a variable.

• It includes a term with a fractional exponent.

What makes g(x) = 5x^5 - 2x^2 a polynomial function?

• It includes a term with a negative exponent.

• It is a difference of two monomials with non-negative integer exponents.

• It has a constant term.

• It includes a square root.

Why is h(x) = 4x^(1/2) + 9 not a polynomial function?

• It includes a term with a fractional exponent.

• It has a constant term.

• It is a sum of two monomials.

• It includes a negative coefficient.

What is the reason j(x) = 7/x + 3 is not a polynomial function?

• It includes a term with a negative exponent.

• It has a constant term.

• It is a sum of two monomials.

• It includes a fractional coefficient.