Question

What are the vertical and horizontal asymptotes for the function f (x) = StartFraction 3 x squared Over x squared minus 4 EndFraction?

Answer 1

Answer:

The vertical asymptotes are x = 2 and x =  -2.

The horizontal asymptote is y = 3.

Step-by-step explanation:

Given the function

$f(x)=\dfrac{3x^2}{x^2-4}$

Rewrite it as follows:

$f(x)\\ \\=\dfrac{3x^2}{x^2-4}\\ \\=3\dfrac{x^2-4+4}{x^2-4}\\ \\=3\left(1+\dfrac{4}{x^2-4}\right)\\ \\=3+\dfrac{12}{(x-2)(x+2)}$

This function is undefined when the denominator is equal to 0. The denominator is equal to 0 when x = 2 or x = -2, so two vertical asymptotes are x = 2 and x =  -2.

The horizontal asymptote is y = 3.

Answer 2

Answer:

A

Step-by-step explanation:

Its the first one on edgeniuty (trash website)