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maria [59]
4 years ago
6

Please help on this one?

Mathematics
1 answer:
Vlad1618 [11]4 years ago
4 0

Answer:

A f(x) is a negative number

Step-by-step explanation:

Lets see what happens

f(x) = 1/x

Let x get smaller and smaller from the negative side

x = -1/2

f(-1/2) = 1/ (-1/2) = -2

x = -1/3

f(-1/3) = 1/ (-1/3) = -3

x = -1/10

f(-1/10) = 1/-1/10 = -10

What is happening

As we get closer to zero from the negative side, f(x) gets  larger and more negative

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The asymptotes of the function are given as follows:

  • Vertical: x = 16.
  • Horizontal: y = 4.

The end behavior is that the function goes to y = 4 both when x goes to negative infinity and when it goes to positive infinity.

<h3>What are the asymptotes of a function f(x)?</h3>

  • The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
  • The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. This also gives the end behavior of f(x).

In this problem, the function is given by:

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For the vertical asymptote, we have that:

x - 16 = 0 -> x = 16.

For the horizontal asymptote, we have that:

y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{4x}{x - 16} = \lim_{x \rightarrow \infty} \frac{4x}{x} = \lim_{x \rightarrow \infty} 4 = 4

Hence the end behavior is that the function goes to y = 4 both when x goes to negative infinity and when it goes to positive infinity.

More can be learned about the asymptotes of a function at brainly.com/question/16948935

#SPJ1

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