Respuesta :
Using the asymptote concept, we have that:
- The vertical asymptote is x = 9.
- The horizontal asymptote is y = 3.
- The end behavior is that as [tex]x \rightarrow \infty, y \rightarrow 3[/tex].
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:
[tex]f(x) = \frac{3x}{x - 9}[/tex]
For the vertical asymptote, we have that:
x - 9 = 0 -> x = 9.
For the horizontal asymptote:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{3x}{x - 9} = \lim_{x \rightarrow \infty} \frac{3x}{x} = \lim_{x \rightarrow \infty} 3 = 3[/tex]
Hence, the end behavior is that as [tex]x \rightarrow \infty, y \rightarrow 3[/tex].
More can be learned about asymptotes at https://brainly.com/question/16948935
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