Characteristics 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?

• Variables can be under a square root.

• All variables must have negative powers.

• All variables must have non-negative integer powers.

• Variables can be in the denominator.

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

• Because it makes the function undefined.

• Because it places the variable in the denominator.

• Because it changes the variable's coefficient.

• Because it turns the variable into a constant.

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

• f(x) = 1/x + 2

• f(x) = 5x^3 + 2x - x^(-1)

• f(x) = sqrt(x) + 3

• f(x) = 3x^2 + 4x + 5

What happens when a variable is placed under a square root in a function?

• It becomes a polynomial.

• It is considered a non-negative integer.

• It remains unchanged.

• It is rewritten as a fractional exponent.

Which of the following is NOT a polynomial function?

• f(x) = 6

• f(x) = x^(1/2) + 5

• f(x) = 7x^3 - 2x + 1

• f(x) = 4x^2 + 3x + 2

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

• Because it includes a square root.

• Because it has a fractional exponent.

• Because it has a variable with a negative power.

• Because it can be rewritten with a variable to the zero power.

What is the power of x in the function f(x) = 8?

• -1

• 1/2

• 0

• 1

Which of the following statements is true about polynomial functions?

• They can have variables under a square root.

• They must have non-negative integer powers.

• They can have fractional powers.

• They can have variables in the denominator.

What is the result of rewriting a variable in the denominator as a power?

• It becomes a positive power.

• It becomes a negative power.

• It becomes a fractional power.

• It becomes zero.

Why is f(x) = x^(-1) not a polynomial function?

• Because it has a variable with a non-negative power.

• Because it has a variable with a fractional power.

• Because it has a variable with a negative power.

• Because it has a variable with a zero power.