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State the horizontal asymptote of the rational function. (f(x) = x^2 + 4x - 7/x - 7)

(A) None
(B) (y = -4)
(C) (y = 7)
(D) (y = 6)

User Piotr Boho
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1 Answer

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Final answer:

The given rational function does not have a horizontal asymptote corresponding to any of the options provided; the correct horizontal asymptote is y=0, so the answer should be (A) None.

The correct answer is A.

Step-by-step explanation:

The horizontal asymptote of a rational function can be determined by examining the degrees of the numerator and the denominator. For the given function f(x) = (x^2 + 4x - 7)/(x - 7), we see that the degree of the numerator is 2 and the degree of the denominator is 1. When the degree of the numerator is one more than the degree of the denominator, the horizontal asymptote is at y equal to the leading coefficient of the numerator divided by the leading coefficient of the denominator.

In this case, the leading coefficient of the numerator is 1 and the leading coefficient of the denominator is 1, hence the horizontal asymptote is y = 0. However, this answer is not listed in the available options, suggesting a mistake in the question or the options provided. The correct answer should be (A) None, since none of the given options match the calculated asymptote.

User Hequ
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