Master Determining if a function is a polynomial or not

The video tutorial explains how to determine if a function is a polynomial by checking if all variable powers are non-negative integers. It provides examples of polynomial and non-polynomial functions, highlighting key rules such as avoiding variables in denominators and under roots. Special cases like constant functions are also discussed, emphasizing that zero power is valid for polynomials.

What is a key characteristic of a polynomial function?

• Variables can be under a root.

• Powers of variables must be non-negative integers.

• Variables can be in the denominator.

• Variables can have negative powers.

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

• f(x) = 1/x

• f(x) = x^-1 + 2

• f(x) = x^2 + 3x + 1

• f(x) = sqrt(x)

Why is the function f(x) = 5/x not considered a polynomial?

• It has a variable in the denominator.

• It has a fractional coefficient.

• It has a variable with a positive power.

• It has a constant term.

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

• Undefined

• 8

• 0

• 1

Why is a function with a variable under a square root not a polynomial?

• The variable is considered to have a fractional power.

• The variable is in the denominator.

• The function has a negative coefficient.

• The function has a constant term.