Polynomial Graphing

What is the degree of the polynomial function f(x) = 3x^4 - 2x^2 + 5?

• 5

• 3

• 2

• 4

Determine the end behavior of the polynomial function g(x) = -2x^3 + 4x^2 - 3x - 1.

• As x approaches positive or negative infinity, g(x) approaches zero.

• As x approaches positive or negative infinity, g(x) approaches a constant value.

• As x approaches positive or negative infinity, g(x) approaches negative infinity.

• As x approaches positive or negative infinity, g(x) approaches positive infinity.

Find the x-intercepts of the polynomial h(x) = x^3 - 4x^2 + 4x.

• x = 1, x = 3

• x = -2, x = 4

• x = 0, x = 2

• x = 5, x = 6

Tags

CCSS.HSF-IF.C.7C

Explain the relationship between the degree of a polynomial and the number of its roots.

• The number of roots of a polynomial is always less than its degree.

• The number of roots of a polynomial is always greater than its degree.

• The number of roots of a polynomial is at most equal to its degree.

• The number of roots of a polynomial is unrelated to its degree.

How does the leading coefficient affect the graph of a polynomial function?

• It affects the symmetry of the graph.

• It affects the x-intercepts of the graph.

• It affects the end behavior of the graph.

• It affects the color of the graph.

Identify the degree of the polynomial function p(x) = 2x^5 - 7x^3 + 4x - 1.

• 7

• 3

• 5

• 2

What is the end behavior of the polynomial function q(x) = 4x^2 - 2x^4 + 3x^3 - 5?

• The end behavior is that the graph falls to the left and rises to the right.

• The end behavior is that the graph rises to the left and rises to the right.

• The end behavior is that the graph rises to the left and falls to the right.

• The end behavior is that the graph falls to the left and falls to the right.

Calculate the x-intercepts of the polynomial function r(x) = x^4 - 6x^2 + 8.

• x = -3, 3

• x = -2, 2

• x = -4, 4

• x = -1, 1

Tags

CCSS.HSA.APR.B.3

Discuss the relationship between the degree of a polynomial and the number of its real roots.

• The number of real roots of a polynomial is unrelated to its degree.

• The number of real roots of a polynomial is at most equal to its degree.

• The number of real roots of a polynomial is always less than its degree.

• The number of real roots of a polynomial is always greater than its degree.

Explain how the leading coefficient affects the graph of a polynomial function.

• The leading coefficient affects the symmetry of the graph

• The leading coefficient determines the x-intercepts of the graph

• The leading coefficient has no effect on the graph

• The leading coefficient affects the end behavior of the graph.