Question

Identify the asymptotes and state the end behavior of the function f(x)=5x/x-25

Answer 1

Using it's concepts, it is found that for the function $f(x) = \frac{5x}{x - 25}$:

• The vertical asymptote of the function is x = 25.

• The horizontal asymptote is y = 5. Hence the end behavior is that $y \rightarrow 5$ when $x \rightarrow \infty$.

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. They also give the end behavior of a function.

In this problem, the function is:

$f(x) = \frac{5x}{x - 25}$

For the vertical asymptote, it is given by:

x - 25 = 0 -> x = 25.

The horizontal asymptote is given by:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = 5$

More can be learned about asymptotes at brainly.com/question/16948935

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