lucalauro
Answered

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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) =

The Graph Shown Here Is The Graph Of Which Of The Following Rational Functions O A FO 23x3 OB AB X 196231x3 X2 O C FX class=

Sagot :

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.

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