Understanding Polynomial Functions

What is a polynomial function?

• A polynomial function is defined as any function that has a constant value.

• A polynomial function is a linear equation of the form y = mx + b.

• A polynomial function is an expression that includes only trigonometric terms.

• A polynomial function is an expression of the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Identify the degree of the polynomial: 3x^4 + 2x^3 - x + 5.

• 3

• 2

• 4

• 5

What is the leading coefficient of the polynomial: 7x^5 - 3x^2 + 2?

• 7

• -3

• 2

• 5

How many roots can a polynomial of degree n have?

• A polynomial of degree n can have at most n roots.

• A polynomial of degree n can have at least n+1 roots.

• A polynomial of degree n can have no roots.

• A polynomial of degree n can have exactly n roots.

What is the general form of a polynomial function?

• f(x) = a_n * x^n + a_(n-1) * x^(n-1) + ... + a_1 * x + a_0

• f(x) = b * x^2 + c * x + d

• f(x) = a * x + b

• f(x) = x^3 + x^2 + x + 1

Evaluate the polynomial f(x) = 2x^2 + 3x - 5 at x = 2.

• 4

• 7

• 9

• 11

What is the difference between a monomial and a polynomial?

• Monomials can have multiple terms while polynomials cannot.

• A monomial is a single term; a polynomial is a sum of multiple terms.

• A monomial is a polynomial with one term.

• A polynomial is always a single term.

If f(x) = x^3 - 4x + 1, what is f(-1)?

• 3

• -2

• 0

• 4

What is the end behavior of the polynomial function f(x) = -2x^3 + 3?

• As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

• As x approaches positive infinity, f(x) approaches zero; as x approaches negative infinity, f(x) approaches zero.

• As x approaches positive infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

• As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

How do you determine if a polynomial is even, odd, or neither?

• Graph the polynomial and observe symmetry.

• Evaluate f(-x) and compare with f(x) and -f(x) to classify the polynomial.

• Count the number of terms in the polynomial.

• Check the degree of the polynomial.