Algebra-2

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

 

A. 

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

 

Asymptotes:

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

 

x-intercept:

Set , then , which implies , so  or . This does not match the graph that the -intercept is at . So this function is incorrect.

 

y-intercept:

Set , we have >1. This does not match the condition that the -intercept is in the range 0 < y < 1. So this function is incorrect.

 

B.Function

Factor the denominator: . So the function becomes .

 

Asymptotes:

Vertical Asymptotes: Set the denominator , we get  and  as the vertical asymptotes, which 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 , which matches the graph.

 

x-intercept:

Set , then , which implies , so . So the -intercept is

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