What is a polynomial function

The video tutorial explains what polynomial functions are, starting with their definition and constraints. It highlights that polynomial functions cannot have negative or rational exponents and provides examples to illustrate valid polynomial functions. The tutorial also presents non-examples, such as absolute value functions and functions with negative or rational exponents, to clarify what does not qualify as a polynomial. The importance of understanding polynomial functions is emphasized for further learning in the course.

What is a necessary condition for a term to be part of a polynomial function?

• The coefficient must be zero.

• The exponent must be a negative integer.

• The exponent must be a non-negative integer.

• The term must include an absolute value.

Which of the following is a polynomial function?

• F(x) = 3x^4 - 5x^3 + 2x^2 + x - 5

• F(x) = x^-2

• F(x) = x^(1/2)

• F(x) = |3x|

In the polynomial function F(x) = 3x^4 - 5x^3 + 2x^2 + x - 5, what is the coefficient of the x^3 term?

• 1

• 2

• -5

• 3

Why is F(x) = |3x| not considered a polynomial function?

• It is a zero function.

• It is an absolute value function.

• It has a rational exponent.

• It has a negative exponent.

Which of the following expressions is not a polynomial function?

• F(x) = x^(1/2)

• F(x) = x^2 + 3x + 1

• F(x) = 2x^3 - x + 4

• F(x) = 7