Algebra-2

We will analyze each function one by one to see which one matches the graph.

 

A.

1. Vertical asymptote:

The vertical asymptote occurs when the denominator is equal to zero. Set , we get . So the vertical asymptote is , which does not match the graph that the vertical asymptote is at . So this function is not the correct one.

 

2. Horizontal asymptote:

To find the horizontal asymptote, we consider the degrees of the polynomial in the numerator and the denominator. 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  of the denominator is also . So is the horizontal asymptote.

 

3. Intercepts:

-intercept: Set , we have , which implies , so .

-intercept: Set , we get

 

 

B.

1. Vertical asymptote:

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

 

2. Horizontal asymptote:

Since the degree of the numerator and the denominator is the same (both are of degree ),  dividing the leading coefficients (both are ), we get as the horizontal asymptote, which also matches the given graph.

 

3. Intercepts:

-intercept: Set , we have , which implies , so .

-intercept: Set , we get

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