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find the horizontal asymptote, if any of the graph of the rational function. g(x)=(21x^2)/(7x^2)+8 select the correct choice below and,

Question

Find the horizontal asymptote, if any of the graph of the rational function. g(x)=(21x^2)/(7x^2)+8 Select the correct choice below and, if necessary, fill in the answer box to complet A. The horizontal asymptote is square . (Type an equation.) B. There is no horizontal asymptote.

Solution

Verificación de expertos
4.5 (203 Votos)
Shirley Mestre · Tutor por 5 anos

Resposta

To find the horizontal asymptote of the rational function \( g(x) = \frac{21x^2}{7x^2 + 8} \), we need to compare the degrees of the polynomial in the numerator and the polynomial in the denominator.1. The degree of the polynomial in the numerator (21 ) is 2.2. The degree of the polynomial in the denominator (7 + 8) is also 2.When the degrees of the numerator and the denominator are equal, the horizontal asymptote is found by dividing the leading coefficients of the numerator and the denominator.The leading coefficient of the numerator is 21, and the leading coefficient of the denominator is 7. Therefore, the horizontal asymptote is: So, the correct choice is:A. The horizontal asymptote is .