Question

Which statement correctly identifies an asymptote of f (x) = StartFraction 16 x squared minus 35 Over x squared minus 5 EndFraction using limits?
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a vertical asymptote at x = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a horizontal asymptote at y = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a vertical asymptote at x = 16.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.

Answer 1

Answer:

D

Step-by-step explanation:

Edge

Answer 2

The limit of x approaching infinite of a function gives it's horizontal assymptote. We use this to solve the question, getting the following answer:

Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.

Horizontal asymptote:

An horizontal asymptote is the value of y given by:

$y = \lim_{x \rightarrow \infty} f(x)$

In this question:

$f(x) = \frac{16x^2 - 35}{x^2 - 5}$

The horizontal asymptote is:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5}$

Considering it is a limit of x going to infinite, we just consider the terms with the highest exponents both in the numerator and in the denominator, so:

$y = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5} = \lim_{x \rightarrow \infty} \frac{16x^2}{x^2} = \lim_{x \rightarrow \infty} 16 = 16$

Thus, the correct answer is:

Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.

From the graph of the function, given at the end of this answer, you can check that as x goes to infinity, y(green line) approches 16(blue line).

For more on infinite limits, you can check brainly.com/question/23335924