Respuesta :
From the asymptotes of the function, the end behavior is given by:
- The vertical asymptote is x = 16.
- The horizontal asymptote is y = 4.
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.
In this problem, the function is given by:
[tex]f(x) = \frac{4x}{x - 16}[/tex]
For the vertical asymptote, it is when the denominator is of zero, hence:
x - 16 = 0 -> x = 16.
For the horizontal asymptote, we find the limit as x goes to infinity, hence:
[tex]\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 given by:
- The vertical asymptote is x = 16.
- The horizontal asymptote is y = 4.
More can be learned about asymptotes and end behavior at https://brainly.com/question/16948935
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