Algebra-2

Let's analyze each function one by one to determine which one matches the given graph:

 

A.Function

First, factor the expressions:

The numerator .

The denominator .

So the function can be written as .

 

Asymptotes:

Vertical Asymptotes: Set the denominator equal to zero, , we get and as the vertical asymptotes. This does not match the graph where the vertical asymptotes are at . So this function is not correct.

 

B.Function

Factor the expressions:

The numerator .

The denominator .

So the function is .

 

Asymptotes:

Vertical Asymptotes: Set the denominator equal to zero, or , giving us and as the vertical asymptotes, which matches the graph.

 

Horizontal Asymptotes: Since the degree of the numerator and the denominator is the same (both are degree 2), we look at the ratio of the leading coefficients. The leading coefficient of the numerator is and of the denominator is also . But due to the negative sign in front, the horizontal asymptote is , which does not match the horizontal asymptote . So this function is not correct.

 

C.Function

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