Question

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) =

Answer 1

Given:

The graph of rational function.

To find:

The rational function.

Solution:

If the graph of a rational function has a vertical asymptote at
`x=a`, then
`(x-a)` 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
`x=-1` and another one is at
`x=3`.

It means,
`(x-3)` and
`(x+1)` are the only two factors of the denominator of the rational function.

In option A, the factors of the denominator are different from
`(x-3)` and
`(x+1)` .

In option B, the denominator has an extra factor
`x-2`.

In option C, the denominator has only two factors
`(x-3)` and
`(x+1)`.

Therefore, the correct option is C.