Question

how all work to identify the asymptotes and state the end behavior of the function f of x is equal to 4x divided by the quantity of x minus 16 end quantity.

Answer 1

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.

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

• 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:

$f(x) = \frac{4x}{x - 16}$

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

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