What are all of the true statements about the function H(x) = (2x – 3)( x2 – 6x + 9)(x + 4)5

It crosses at the root x = 1.5.

It bounces off of the x-axis at (3, 0)

It's end behavior is from negative infinity to negative infinity.

Pre-calculus Quiz Graphing Polynomials

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| By Kat Ahrens

Kat Ahrens

Community Contributor

Quizzes Created: 1 | Total Attempts: 45

Questions: 4 | Attempts: 45 | Updated: Mar 17, 2023

1.

Please graph the following function and upload it. f(x) - H(x) = (x – 3)( x² – 6x + 9)(x + 4)⁵
2.

Describe the graph of the polynomial function P(x) = -2(x² – 16)(x³- 4x)
3.

F(x) = -4x⁷ – 5x⁵ + 3x² – 14x -2 is a polynomial of degree ________ and it's end behavior goes from________ infinity to ________ infinity.

Explanation
The given polynomial is of degree seven because the highest exponent of x in the polynomial is seven. The end behavior of the polynomial is odd because the leading coefficient is negative. As x approaches negative infinity, the polynomial goes to positive infinity, and as x approaches positive infinity, the polynomial goes to negative infinity. Therefore, the end behavior of the polynomial goes from positive infinity to negative infinity.

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4
4.

What are all of the true statements about the function H(x) = (2x – 3)( x² – 6x + 9)(x + 4)⁵
- A.
  
  It crosses at the root x = 1.5.
- B.
  
  It is an even function.
- C.
  
  It's end behavior is from negative infinity to negative infinity.
- D.
  
  It crosses the x axis at x = 4
- E.
  
  It bounces off of the x-axis at (3, 0)
Correct Answer(s)
A. It crosses at the root x = 1.5.
B. It is an even function.
E. It bounces off of the x-axis at (3, 0)

Explanation
The function H(x) = (2x – 3)(x2 – 6x + 9)(x + 4)5 crosses at the root x = 1.5 because when x = 1.5, the value of the function is not equal to zero. The function is an even function because it is symmetric with respect to the y-axis. It bounces off of the x-axis at (3, 0) because the function changes sign from negative to positive at that point.

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5.

The function has an ________ degree, with ________ root(s) that have odd multiplicity and ________ root(s) that have even multiplicity.

Correct Answer(s)
even
four, 4
one, 1

Explanation
The function has an even degree, which means that the highest power of the variable in the function is an even number. The function has four roots, each with a multiplicity of 4, indicating that each root appears 4 times in the function. Additionally, the function has one root with a multiplicity of 1, meaning that this particular root appears only once in the function.

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4

Pre-calculus Quiz Graphing Polynomials

Please graph the following function and upload it. f(x) - H(x) = (x – 3)( x² – 6x + 9)(x + 4)⁵

Describe the graph of the polynomial function P(x) = -2(x² – 16)(x³- 4x)

F(x) = -4x⁷ – 5x⁵ + 3x² – 14x -2 is a polynomial of degree and it's end behavior goes from infinity to infinity.

What are all of the true statements about the function H(x) = (2x – 3)( x² – 6x + 9)(x + 4)⁵

The function has an degree, with root(s) that have odd multiplicity and root(s) that have even multiplicity.

Pre-calculus Quiz Graphing Polynomials

Please graph the following function and upload it. f(x) - H(x) = (x – 3)( x2 – 6x + 9)(x + 4)5

Describe the graph of the polynomial function P(x) = -2(x2 – 16)(x3- 4x)

F(x) = -4x7 – 5x5 + 3x2 – 14x -2 is a polynomial of degree ________ and it's end behavior goes from________ infinity to ________ infinity.