Question

Which of the following rational functions is graphed below?

Answer 1

Answer:

A. $f(x) = \frac{x-1}{x\cdot (x-3)}$

Step-by-step explanation:

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

$f(x) = \frac{p(x)}{q(x)}$ (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 $f(x) = \frac{x-1}{x\cdot (x-3)}$. (Correct answer: A)