Question

Which of the following rational functions is graphed below?

Answer 1

`\textsf{D.}\quad f(x)=((x-1))/(x(x-3))`

Explanation:

An asymptote is a line that the curve gets infinitely close to, but never touches.

Vertical asymptotes of a rational function occur when the denominator equals zero.

From inspection of the given graph, the vertical asymptotes are:

• x = 0
• x = 3

Therefore, for the denominator to equal zero, it must include the factors:

• x
• (x - 3)

Since the only answer option that has the factors x and (x - 3) is option D, the graphed rational function is:

`f(x)=((x-1))/(x(x-3))`