Given:
The graph of rational function.
To find:
The rational function.
Solution:
If the graph of a rational function has a vertical asymptote at [tex]x=a[/tex], then [tex](x-a)[/tex] 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 [tex]x=-1[/tex] and another one is at [tex]x=3[/tex].
It means, [tex](x-3)[/tex] and [tex](x+1)[/tex] are the only two factors of the denominator of the rational function.
In option A, the factors of the denominator are different from [tex](x-3)[/tex] and [tex](x+1)[/tex] .
In option B, the denominator has an extra factor [tex]x-2[/tex].
In option C, the denominator has only two factors [tex](x-3)[/tex] and [tex](x+1)[/tex].
Therefore, the correct option is C.
