what are the vertical and horizontal asymptotes for the function f(x)=3x²/(x² - 4)? horizontal asymptote: y…

what are the vertical and horizontal asymptotes for the function f(x)=3x²/(x² - 4)? horizontal asymptote: y = -2, y = 2 vertical asymptote: x = 3 horizontal asymptote: y = -4, y = 1 vertical asymptote: x = 3 horizontal asymptote: y = 3 vertical asymptote: x = -4, x = 1 horizontal asymptote: y = 3 vertical asymptote: x = -2, x = 2

what are the vertical and horizontal asymptotes for the function f(x)=3x²/(x² - 4)? horizontal asymptote: y = -2, y = 2 vertical asymptote: x = 3 horizontal asymptote: y = -4, y = 1 vertical asymptote: x = 3 horizontal asymptote: y = 3 vertical asymptote: x = -4, x = 1 horizontal asymptote: y = 3 vertical asymptote: x = -2, x = 2

Answer

Explanation:

Step1: Find vertical asymptotes

Set denominator equal to 0. So, $x^{2}-4 = 0$. Factoring gives $(x + 2)(x - 2)=0$. Solving for $x$: $x=-2$ or $x = 2$.

Step2: Find horizontal asymptotes

Since the degree of the numerator and denominator are the same (both degree 2), divide the leading - coefficients. The leading coefficient of the numerator is 3 and of the denominator is 1. So, $y=\frac{3}{1}=3$.

Answer:

D. horizontal asymptote: $y = 3$, vertical asymptote: $x=-2,x = 2$