Algebra-2

To analyze the graph of the function , we can break down its characteristics:

 

1. As  approaches positive or negative infinity (), the term  approaches . Thus, the entire function  approaches .

 

2. The vertical asymptote occurs when the denominator  is equal to zero. Solving , we find .

   - As  approaches  from the left (values less than 2),  is negative and getting closer to . So,  approaches positive infinity, and  approaches .

   - As  approaches  from the right (values greater than 2),  is positive and getting closer to . Therefore,  approaches negative infinity, and