To find the horizontal asymptote of the rational function \( g(x) = \frac{16x^2}{8x^2 + 7} \), we consider the degrees of the polynomial in the numerator and the polynomial in the denominator.
- The degree of the numerator (16x^2) is 2.
- The degree of the denominator (8x^2 + 7) is also 2.
According to the rules for horizontal asymptotes for rational functions:
- If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is \( y = 0 \).
- If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is given by the ratio of the leading coefficients.
Since both the numerator and the denominator have the same degree (2), we will use the leading coefficients:
- The leading coefficient of the numerator (16x^2) is 16.
- The leading coefficient of the denominator (8x^2) is 8.
Thus, the horizontal asymptote is:
\[ y = \frac{16}{8} = 2 \]
So, the horizontal asymptote of the graph of the function is:
A. The horizontal asymptote is \( y = 2 \).
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