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zhuklara
11 days ago
12

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

ction?

Mathematics
2 answers:
Leona [4.1K]11 days ago
7 0

Answer:

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

The horizontal asymptote is located at y = 3.

Step-by-step explanation:

Given the function

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

Transform it into the following:

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 not defined when the denominator equals zero. This occurs when x = 2 or x = -2, resulting in two vertical asymptotes located at x = 2 and x = -2.

<pThe horizontal asymptote is determined to be y = 3.

lawyer [4K]11 days ago
6 0

Answer:

A

Step-by-step explanation:

This is the first item listed on Edgeniuty (an unreliable site).

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