Considering the asymptotes, the rational function given below is the following:
B. [tex]f(x) = \frac{1}{x(x + 2)}[/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.
From the graph, the vertical asymptotes are x = 0 and x = -2, hence the denominator is given by:
x(x + 2).
The function has no x-intercepts, hence the numerator is of 1. So the function is given by:
B. [tex]f(x) = \frac{1}{x(x + 2)}[/tex]
More can be learned about asymptotes at https://brainly.com/question/16948935
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