Algebra-2

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

 

A.

1. Simplification:

First, factor the denominator . So the function can be written as (for ).

 

2. Vertical asymptote:

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

 

3. Horizontal asymptote:

Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is , which meets the graph.

 

4. -intercept:

Set , we get . Since -1<<0, it satisfies the condition for the -intercept.

 

5. Monotonicity:

The derivative of is .  For all , y'<0, which means the function is decreasing on its domain. So it is a gradually decreasing function as required.

 

B.

1. Simplification:

Factor the numerator . Then the function becomes (for ).

 

2. Vertical asymptote:

Set

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