what are the vertical and horizontal asymptotes for the function $f(x)=\frac{3x^{2}}{x^{2}-4}$?\no…

what are the vertical and horizontal asymptotes for the function $f(x)=\frac{3x^{2}}{x^{2}-4}$?\no horizontal asymptote: $y = - 2,y = 2$\nvertical asymptote: $x = 3$\no horizontal asymptote: $y=-4,y = 1$\nvertical asymptote: $x = 3$\no horizontal asymptote: $y = 3$\nvertical asymptote: $x=-4,x = 1$\no horizontal asymptote: $y = 3$\nvertical asymptote: $x=-2,x = 2$

what are the vertical and horizontal asymptotes for the function $f(x)=\frac{3x^{2}}{x^{2}-4}$?\no horizontal asymptote: $y = - 2,y = 2$\nvertical asymptote: $x = 3$\no horizontal asymptote: $y=-4,y = 1$\nvertical asymptote: $x = 3$\no horizontal asymptote: $y = 3$\nvertical asymptote: $x=-4,x = 1$\no horizontal asymptote: $y = 3$\nvertical asymptote: $x=-2,x = 2$

Answer

Answer:

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

Explanation:

Step1: Find vertical asymptotes

Set denominator equal to 0. $x^{2}-4=0$

Step2: Solve for x

Factor the equation: $(x + 2)(x - 2)=0$. Then $x=-2$ or $x = 2$.

Step3: Find horizontal asymptote

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