Algebra-2

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

 

A. Analyze the function

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

 

Vertical asymptotes: The vertical asymptotes occur when the denominator is equal to zero. Setting , we get . So the vertical asymptote is at , not  and  as required, so this function does not match.

 

B. Analyze the function

Factor the denominator: . So the function becomes:

 

Vertical asymptotes: Setting the denominator equal to zero, we have  or , which gives us vertical asymptotes at  and .

 

Horizontal asymptote: Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is .

 

x-intercept: Set , then , so , which means the function intersects the -axis at .

 

y-intercept: To find the -intercept, set , then , and 0<

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