Algebra-2

Let's analyze each function one by one to see which one matches the given graph.

 

A. Analyze the function

First, we factor the denominator: . Then the function can be rewritten as:

When , the original function is undefined because the denominator becomes , which creates a hole at .

When , . Also, the function  is a hyperbola and not a straight line passing through the origin, so this function does not match the graph.

 

B. Analyze the function

Factor out  from the numerator: . Then the function becomes:

When , the function is undefined, creating a hole at .

When , . So this function does not match the graph.

 

C. Analyze the function

Factor the numerator:

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