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This printable supports Common Core Mathematics Standard HSF-IF.C.7, HSF-IF.C.7c

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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.
  1. True
  2. False
2. 
When graphing a polynomial function of degree 8, whose leading coefficient is -3, which of the following is correct?
  1. The function tends toward positive infinity as x approaches negative and positive infinity.
  2. The function tends toward negative infinity as x approaches negative and positive infinity.
  3. The function tends toward negative infinity as x approaches negative infinity, and the function tends toward positive infinity as x approaches positive infinity.
  4. 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.
  1. [math]x^4 + 7x^3 - 37x^2 - 255x - 548[/math]
  2. [math]x^4 - 9x^3 -21x^2 +209x-180[/math]
  3. [math]x^4 - 9x^3 - 21x^2 - 127x + 2508[/math]
  4. [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].
  1. [math]x^3 - 18x^2 + 141x - 1060[/math]
  2. [math]x^3 - 18x^2 - 183x - 1438[/math]
  3. [math]x^3 - 21x + 20[/math]
  4. [math]x^2 - 8x + 43[/math]
C. 
What are the remaining zeros of the function P(x)?
  1. -5, 1, and 4
  2. There are no more zeros.
  3. 1 and 4
  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?
  1. -10, -9, ..., 9, 10
  2. -1,000, -900, ..., 900, 1,000
  3. -5,000, -4,500, ..., 4,500, 5000
  4. -10,000, -9,000, ...., 9,000, 10,000
F. 
Graph the function [math]P(x)[/math].
Graph 10x10



4. 
Graph: [math] y=2x^3-8x [/math]
Graph 10x10



5. 
Graph: [math]y=x(x+2)^2[/math]
Graph 10x10



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