# Pre-calculus Quiz Graphing Polynomials

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Kat Ahrens
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• 1.

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• 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.

### 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)

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.

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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• Current Version
• Mar 17, 2023
Quiz Edited by
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• Mar 13, 2020
Quiz Created by
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