Lesson 8

End Behavior (Part 1)

Problem 1

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

Solution

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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:

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

Solution

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Problem 3

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

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.

Solution

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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?

Solution

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(From 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. $$g(x)=\text-2(3x+1)(x+2)(x-3)$$

Solution

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(From 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?

Solution

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(From 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 $$f(x)$$?

Solution

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(From Unit 2, Lesson 7.)