Answer:
A. [tex]f(x) = \frac{x-1}{x\cdot (x-3)}[/tex]
Step-by-step explanation:
A rational-polynomic function is a function of the form:
[tex]f(x) = \frac{p(x)}{q(x)}[/tex] (1)
There are three important remarks on this kind of function:
1) [tex]p(x) = 0[/tex] when function passes through the x-axis.
2) If [tex]q(x) = 0[/tex], then the function [tex]f(x)[/tex] has a vertical asymptote.
3) The horizontal asymptote is a linear function of the form [tex]y = \lim_{x \to \pm \infty} f(x)[/tex].
In accordance with the graph, the function has two vertical asymptotes at [tex]x = 0[/tex] and [tex]x = 3[/tex], numerator becomes zero for [tex]x = 1[/tex] and horizontal asymptote is [tex]y = 0[/tex] as grade of numerator is less than grade of denominator.
Hence, we conclude that rational function is [tex]f(x) = \frac{x-1}{x\cdot (x-3)}[/tex]. (Correct answer: A)
