Problem

c. The function $f(x)=\frac{x+4000}{x^{2}-7}$ has a horizontal asymptote at...
\[
y=
\]
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Answer

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Answer

\(\boxed{y=0}\)

Steps

Step 1 :The horizontal asymptote of a function can be found by looking at the degree of the polynomial in the numerator and the denominator. If the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is at y=0. If the degrees are equal, the horizontal asymptote is at the ratio of the leading coefficients. If the degree of the numerator is greater, there is no horizontal asymptote.

Step 2 :In this case, the degree of the denominator (2) is greater than the degree of the numerator (1), so the horizontal asymptote should be at y=0.

Step 3 :The horizontal asymptote of the function \(f(x)=\frac{x+4000}{x^{2}-7}\) is at \(y=0\).

Step 4 :\(\boxed{y=0}\)

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