Characteristics and Examples of Polynomial Functions

The video tutorial explains how to determine if a function is a polynomial by checking if all variables have non-negative integer powers. It provides examples of polynomial and non-polynomial functions, highlighting common misconceptions and special cases. The key rules include ensuring variables are not in the denominator or under a root, and powers must be non-negative integers.

What is the primary characteristic of a polynomial function?

• All variables must have negative powers.

• All variables must be in the denominator.

• All variables must have non-negative integer powers.

• All variables must be under a square root.

Why can't variables in a polynomial have negative powers?

• Because they would be in the denominator.

• Because they would be in the numerator.

• Because they would be under a square root.

• Because they would be fractions.

Which of the following is an example of a polynomial function?

• 5x^3 + 2x - x^-1

• 3x^2 + 4x + 5

• 1/x + 3x^2

• x^(1/2) + 2x

What is the role of coefficients in determining if a function is a polynomial?

• Coefficients must be integers.

• Coefficients must be non-negative.

• Coefficients must be positive.

• Coefficients do not affect polynomial status.

Why is f(x) = 8 considered a polynomial?

• Because it is a constant function.

• Because it has a variable with a fractional power.

• Because it has a variable with a negative power.

• Because it can be written as x^0, which is a non-negative integer.

What happens if a variable is under a square root in a function?

• It is considered a non-negative integer.

• It is not considered a polynomial.

• It becomes a positive integer.

• It becomes a polynomial.

Which of the following is NOT a polynomial function?

• x^3 + 2x^2 + x

• x^2 + 1/x

• 2x^4 + 3x^3

• x^5 + 4x + 7

What is the significance of the power being a non-negative integer in polynomials?

• It ensures the function is negative.

• It ensures the function is a fraction.

• It ensures the function is a polynomial.

• It ensures the function is a square root.

How can a variable in the denominator affect the polynomial status of a function?

• It makes the function a polynomial.

• It makes the power a non-negative integer.

• It makes the function not a polynomial.

• It has no effect on the polynomial status.

What is the effect of having a fractional power in a function?

• It makes the function a fraction.

• It makes the function a square root.

• It makes the function a polynomial.

• It makes the function not a polynomial.