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: its d

Step-by-step explanation: nobody reading all that

Answer 2

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

The horizontal asymptote is y = 3.

Explanation:

Given the function

`f(x)=(3x^2)/(x^2-4)`

Rewrite it as follows:

`f(x)\\ \\=(3x^2)/(x^2-4)\\ \\=3(x^2-4+4)/(x^2-4)\\ \\=3\left(1+(4)/(x^2-4)\right)\\ \\=3+(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.