Considering it's asymptotes, the rational function shown in the graph is:
C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/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 graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:
(x + 2)(x - 1).
The horizontal asymptote is of y = 0, hence the function can be given by:
C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]
More can be learned about rational functions and asymptotes at https://brainly.com/question/24410059
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