Answer :
Using the asymptote concept, it is found that:
- The vertical asymptote is of x = 25.
- The horizontal asymptote is of y = 5.
- Considering the horizontal asymptote, it is found that the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.
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{5x}{x - 25}[/tex]
Considering the denominator, the vertical asymptote is:
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 of the function is that it tends to y = 5 to the left and to the right of the graph.
More can be learned about asymptotes and end behavior at https://brainly.com/question/28037814
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