Pre-calculus Quiz Graphing Polynomials

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Quizzes Created: 1 | Total Attempts: 53

| Attempts: 53 | Questions: 3 | Updated: Jan 22, 2025

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1) 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 is an even function.

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

It crosses the x axis at x = 4

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

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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About This Quiz

Pre-calculus Quiz Graphing Polynomials - Quiz

This Pre-Calculus Quiz on Graphing Polynomials assesses skills in graphing polynomial functions and understanding their properties. It includes problems on polynomial degrees, end behaviors, roots, and graph descriptions, enhancing learners' comprehension of polynomial behaviors in algebraic contexts.

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

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

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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