Math Problem Statement

Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?

Solution

To determine which graph shows the same end behavior as the function f(x)=2x6−2x2−5f(x) = 2x^6 - 2x^2 - 5, we need to analyze the dominant term in the polynomial because it dictates the end behavior.

Key Points:

  1. Degree of the Polynomial:
    The function f(x)=2x6−2x2−5f(x) = 2x^6 - 2x^2 - 5 is a polynomial of degree 6. The highest degree term is 2x62x^6.

  2. Leading Term and End Behavior:
    The leading term 2x62x^6 dominates the end behavior of the function as xx becomes very large

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Math Problem Analysis

Mathematical Concepts

Polynomials
End behavior of polynomials

Formulas

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Theorems

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Suitable Grade Level

Grades 11-12

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