Understanding Polynomial Functions Concepts

The video tutorial introduces polynomial functions, explaining their structure, including variables, powers, and coefficients. It discusses the standard form and degree of polynomials, and examines the anatomy of polynomial functions by detailing terms and coefficients. The video also tests and identifies polynomial functions, providing examples of functions that are and are not polynomials. The tutorial concludes with a brief mention of the next topic, rational functions.

What is a key characteristic of the powers of X in a polynomial function?

• They can be any real number.

• They must be fractional.

• They are always negative.

• They are unique and non-repeating.

In a polynomial function, what type of powers can X have?

• Only positive integers

• Any real number

• Non-negative integers

• Negative integers

What is the standard form of a polynomial function?

• Terms arranged alphabetically

• Terms arranged in random order

• Terms arranged in decreasing powers of X

• Terms arranged in increasing powers of X

What determines the degree of a polynomial function?

• The constant term

• The number of terms in the function

• The highest power of X with a non-zero coefficient

• The sum of all coefficients

What is the leading coefficient in a polynomial function?

• The first coefficient in the function

• The coefficient of the term with the highest power

• The coefficient of the term with the lowest power

• The coefficient of the constant term

What is the term for the coefficient of X raised to the power of 0?

• Leading term

• Quadratic term

• Linear term

• Constant term

Which of the following is NOT a polynomial function?

• f(x) = 3x^2 + 2x + 1

• f(x) = 2x^4/5 + 2

• f(x) = x^4 + x

• f(x) = 5

Why is the function f(x) = 6/x^2 not considered a polynomial?

• It has a negative power.

• It has a constant term.

• It has a fractional power.

• It has a linear term.

Can a polynomial function have missing X terms?

• Yes, but only if the degree is even.

• Yes, a polynomial can have missing terms.

• No, it must have at least one term for each power.

• No, all terms must be present.

What is the degree of the polynomial function f(x) = x^4 + x?

• 2

• 1

• 3

• 4