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