Algebra-2

To derive the equation of the function based on the given properties, we will analyze the transformations applied to the original function .

 

1.Vertical Asymptote: The function approaches as x approaches -2 from the left and  as x approaches -2 from the right. This indicates a vertical asymptote at x = -2, suggesting a horizontal shift to the left. Thus, we replace x with x + 2.

 

2.Horizontal Asymptote: The graph approaches 1 as x approaches . This means there is a vertical shift upward, so we add 1 to the function.

 

Putting these transformations together, we start with and apply the shifts:

Replace x with x + 2 for the horizontal shift:

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