# Graphing Polynomial Functions (Grades 11-12)

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## Graphing Polynomial Functions

**Instructions:**
Ensure that all graphs are labeled correctly.

1.

When graphing a polynomial function of degree n, there will always be n distinct x-intercepts.

- True
- False

2.

When graphing a polynomial function of degree 8, whose leading coefficient is -3, which of the following is correct?

- The function tends toward positive infinity as x approaches negative and positive infinity.
- The function tends toward negative infinity as x approaches negative and positive infinity.
- The function tends toward negative infinity as x approaches negative infinity, and the function tends toward positive infinity as x approaches positive infinity.
- The function tends toward positive infinity as x approaches negative infinity, and the function tends toward negative infinity as x approaches positive infinity.

3.

Consider the polynomial function [math]P(x) = x^5 - x^4 - 93x^3 + 41x^2 + 1492x - 1440[/math] for the following questions.

A.

Using polynomial long division, find the resulting polynomial if -8 is a zero of the function.

- [math]x^4 + 7x^3 - 37x^2 - 255x - 548[/math]
- [math]x^4 - 9x^3 -21x^2 +209x-180[/math]
- [math]x^4 - 9x^3 - 21x^2 - 127x + 2508[/math]
- [math]x^4 +7x^3 - 149x^2 + 1233x - 8354[/math]

B.

Using the result from the previous question, and the fact that 9 is also a zero of the function [math]P(x)[/math], use polynomial division to find the result of [math](P(x))/((x+8)*(x-9))[/math].

- [math]x^3 - 18x^2 + 141x - 1060[/math]
- [math]x^3 - 18x^2 - 183x - 1438[/math]
- [math]x^3 - 21x + 20[/math]
- [math]x^2 - 8x + 43[/math]

C.

What are the remaining zeros of the function P(x)?

- -5, 1, and 4
- There are no more zeros.
- 1 and 4
- -5 and 4

D.

What is the end behavior of P(x)? Select how the function P behaves as x approaches negative infinity and as x approaches positive infinity.

[math]P -> -oo[/math] | [math]P-> +oo[/math] | |

[math]x -> -oo[/math] | ||

[math]x -> +oo[/math] |

E.

When graphing P(x), which of the following would be the best scale for the y-axis?

- -10, -9, ..., 9, 10
- -1,000, -900, ..., 900, 1,000
- -5,000, -4,500, ..., 4,500, 5000
- -10,000, -9,000, ...., 9,000, 10,000

F.

Graph the function [math]P(x)[/math].

4.

Graph: [math] y=2x^3-8x [/math]

5.

Graph: [math]y=x(x+2)^2[/math]

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