Question

What are the vertical and horizontal asymptotes for the function f (x) = startfraction 3 x squared over x squared minus 4 endfraction? 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 1

Answer:

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horizontal asymptote: y = 3

vertical asymptote: x = –2, x = 2

Step-by-step explanation:

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Answer 2

Using it's concepts, it is found that the vertical and horizontal asymptotes for the function f (x) are given by:

x = -2, x = 2, y = 3.

What are the asymptotes of a function f(x)?

• The vertical asymptotes is composed by the values of the input x which are not in the function's domain.

• The horizontal asymptote is the limit of f(x) as x goes to infinity..

In this problem, the function is given by:

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

For the vertical asymptotes, we have that the denominator cannot be zero, hence:

$x^2 - 4 = 0 \rightarrow x = \pm \sqrt{4} \rightarrow x = \pm 2$

For the horizontal asymptote, we have that:

$y = \lim_{x \rightarrow \infty} \frac{3x^2}{x^2 - 4} = 3$

Hence the asymptotes are given by:

x = -2, x = 2, y = 3.

More can be learned about asymptotes at brainly.com/question/16948935

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