Question

Which of the following rational functions is graphed below?

Answer 1

A.
`f(x) = (x-1)/(x\cdot (x-3))`

Explanation:

A rational-polynomic function is a function of the form:

`f(x) = (p(x))/(q(x))` (1)

There are three important remarks on this kind of function:

1)
`p(x) = 0` when function passes through the x-axis.

2) If
`q(x) = 0`, then the function
`f(x)` has a vertical asymptote.

3) The horizontal asymptote is a linear function of the form
`y = \lim_(x \to \pm \infty) f(x)`.

In accordance with the graph, the function has two vertical asymptotes at
`x = 0` and
`x = 3`, numerator becomes zero for
`x = 1` and horizontal asymptote is
`y = 0` as grade of numerator is less than grade of denominator.

Hence, we conclude that rational function is
`f(x) = (x-1)/(x\cdot (x-3))`. (Correct answer: A)