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d1i1m1o1n [39]
3 years ago
12

PLEASE HELP ILL GIVE BRAINLIEST

Mathematics
1 answer:
cluponka [151]3 years ago
6 0

Answer:

\displaystyle f(x)=\frac{1}{x(x-3)}

Option C.

Step-by-step explanation:

<u>Asymptotes Of A Rational Function</u>

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

\boxed{\displaystyle f(x)=\frac{1}{x(x-3)}}

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