Algebra-2

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

 

A.

1. Vertical asymptote:

To find the vertical asymptote, we set the denominator equal to zero. For , when , we get . This does not match the graph that the vertical asymptote is at . So this function is not correct.

 

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 matches the horizontal asymptote condition, but due to the incorrect vertical asymptote, it doesn't represent the given graph.

 

3. Intercepts:

-intercept: Set , we have , which implies , so . This does not match the graph that the -intercept is at .

-intercept: Set , we get .

 

B.

1. Vertical asymptote:

Set , we find . This satisfies the condition for the vertical asymptote.

 

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 meets  the horizontal asymptote of the given graph.

 

3. Intercepts:

-intercept: Set

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