The graph shown here is the graph of which of the following rational functions
O A FO) = 2-3x+3
OB. AB) = x= 1962–31x-3
x-2
O C. FX) =

Given:

The graph of rational function.

To find:

The rational function.

Solution:

If the graph of a rational function has a vertical asymptote at , then must be a factor of the denominator of that rational function.

From the given graph it is clear that the graph has two vertical asymptotes. One is at and another one is at .

It means, and are the only two factors of the denominator of the rational function.

In option A, the factors of the denominator are different from and .

In option B, the denominator has an extra factor .

In option C, the denominator has only two factors and .

Therefore, the correct option is C.