Respuesta :
Considering the given function and the asymptote concept, we have that:
- The vertical asymptote is of x = 25.
- The horizontal asymptote is of y = 5.
- The end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/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. Hence it also gives the end behavior of the function.
In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex].
The vertical asymptote is found as follows:
x - 25 = 0 -> x = 25.
The horizontal asymptote is found as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5[/tex].
Hence the end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].
More can be learned about asymptotes at https://brainly.com/question/16948935
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