Answer:
[tex]\displaystyle f(x)=\frac{1}{x(x-3)}[/tex]
Option C.
Step-by-step explanation:
Asymptotes Of A Rational Function
We can easily recognize if x=a is a vertical asymptote of a given function f(x) because its graph tends to quickly increase or decrease getting closer to the vertical line x=a but never actually touching it.
We can see in the graph provided, there are two vertical lines, one at x=0 and the other at x=3 (assuming the x-scale is 2). It means the denominator tends to zero at both of those values, i.e. there must be factors like (x-0)(x-3)=x(x-3). The only option with these characteristics is the last one
[tex]\boxed{\displaystyle f(x)=\frac{1}{x(x-3)}}[/tex]
