Algebra-2

Let's analyze each function one by one based on the graph:

 

A.

1. Simplification and nature:

This function simplifies to  (for ), because the numerator and denominator are the same and can be canceled out. But it represents a horizontal line  rather than a hyperbola, so it does not match the graph.

 

B.

1. Vertical asymptote:

Set the denominator , we get . So the vertical asymptote is at , which matches the given graph.

 

2. Horizontal asymptote:

Since the degree of the numerator and the denominator is the same (both are of degree ), we divide the leading coefficients. The leading coefficient of the numerator is  and that of the denominator is . So , which does not match the graph that the horizontal asymptote is at .

 

C.

1. Vertical asymptotes:

First, factor the denominator

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