Lesson 8

End Behavior (Part 1)

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Match each polynomial with its end behavior. Some end behavior options may not have a matching polynomial.

Problem 2

Which polynomial function gets larger and larger in the negative direction as \(x\) gets larger and larger in the negative direction?

A:

$f(x) = 5x^2 - 2x + 1$

B:

$f(x) = 6x^3 + 4x^2 -15x + 32$

C:

$f(x) = 7x^4 - 2x^3 + 3x^2 + 8x - 10$

D:

$f(x) = 8x^6 + 1$

Problem 3

The graph of a polynomial function \(f\) is shown. Which statement about the polynomial is true?

polynomial function graphed. x intercepts = -2, -1, 1, 2. y intercept = 3 point 5. f of x increases as x increases in both the positive and negative direction.
A:

The degree of the polynomial is even.

B:

The degree of the polynomial is odd.

C:

The constant term of the polynomial is even.

D:

The constant term of the polynomial is odd.

Problem 4

Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece of poster board and then folding up the sides. The volume \(V(x)\) in cubic inches of the open-top box is a function of the side length \(x\) in inches of the square cutouts.

  1. Write an expression for \(V(x)\).
  2. What is the volume of the box when \(x=6\)?
  3. What is a reasonable domain for \(V\) in this context?
(From Algebra2, Unit 2, Lesson 1.)

Problem 5

For each polynomial function, rewrite the polynomial in standard form. Then state its degree and constant term.

  1. \(f(x)=(3x+1)(x+2)(x-3)\)
  2. \(g(x)=\text-2(3x+1)(x+2)(x-3)\)
(From Algebra2, Unit 2, Lesson 6.)

Problem 6

Kiran wrote \(f(x)=(x-3)(x-7)\) as an example of a function whose graph has \(x\)-intercepts at \(x=\text-3,\text-7\). What was his mistake?

(From Algebra2, Unit 2, Lesson 7.)

Problem 7

A polynomial function, \(f(x)\), has \(x\)-intercepts at \((\text-6, 0)\) and \((2, 0)\). What is one possible factor of \(f(x)\)?

(From Algebra2, Unit 2, Lesson 7.)