Problem

Find the horizontal asymptote of the given function.
\[
g(x)=\frac{x^{2}+8 x-8}{x-8}
\]
A. $y=-8$
B. $y=8$
C. $y=0$
D. None

Answer

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Answer

Final Answer: \(\boxed{\text{D. None}}\)

Steps

Step 1 :Find the horizontal asymptote of the given function. \[g(x)=\frac{x^{2}+8 x-8}{x-8}\]

Step 2 :The horizontal asymptote of a rational function can be found by comparing the degrees of the numerator and denominator.

Step 3 :If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0.

Step 4 :If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients.

Step 5 :If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Step 6 :In this case, the degree of the numerator is 2 and the degree of the denominator is 1.

Step 7 :Therefore, there is no horizontal asymptote.

Step 8 :Final Answer: \(\boxed{\text{D. None}}\)

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