Respuesta :
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:
[tex]f(x) = \frac{4x}{x - 16}[/tex]
For the vertical asymptote, we have that:
x - 16 = 0 -> x = 16.
For the horizontal asymptote, we have that:
[tex]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[/tex]
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 https://brainly.com/question/16948935
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