High School

An end behavior model for [tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex] is [tex]g(x) =[/tex]

A. [tex]2x^2[/tex]
B. [tex]2x^3[/tex]
C. [tex]2x^4[/tex]
D. [tex]2x^6[/tex]

Answer :

Final answer:

The end behavior model for the given polynomial function is g(x) = 2x⁶. Therefore the correct option is d.

Explanation:

The end behavior of a polynomial function is determined by the degree and the leading coefficient of the function. In this case, the polynomial function is f(x) = 8x⁶ - 16x³ + 8/4x² - 4x - 24. The degree of the function is 6, which means the highest power of x is 6.

The leading coefficient is 8, which is the coefficient of the term with the highest power of x. Therefore, the end behavior model for this function is g(x) = d. 2x⁶.

Learn more about Polynomial functions here:

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