Algebra-2

Let's analyze the function  step by step to determine which graph is correct:

 

1. Factorization

First, factor the denominator:

So the function can be written as .

 

 2. Asymptotes

Vertical Asymptotes:

Set the denominator equal to zero, , which gives  and . So, there are vertical asymptotes at  and .

 

Horizontal Asymptotes:

Since the degree of the polynomial in the numerator (degree ) is less than the degree of the polynomial in the denominator (degree ), by the rules for finding horizontal asymptotes of rational functions, the horizontal asymptote is .

 

 3. Intercepts

x-intercept:

Set , we have , which implies , so . Thus, the -intercept is .

 

y-intercept:

Set