Algebra-2

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

 

A.Function

First, factor the denominator: . So the function can be written as .

 

Asymptotes:

Vertical Asymptotes: Set the denominator equal to zero, , which gives  and  as the vertical asymptotes. This matches the graph.

 

Horizontal Asymptotes: Since the degree of the numerator  (degree ) is less than the degree of the denominator  (degree ), by the rules for finding horizontal asymptotes of rational functions, the horizontal asymptote is . This also matches the graph.

 

y-intercept:

Set , then , and 0 < < 1. So the -intercept also matches the given graph.

 

B.Function

Asymptotes:

Vertical Asymptote: Set

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