Algebra-2

To find the equation of the function based on the properties you provided, we analyze the transformations of the original function .

 

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

 

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

 

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

Replace x with x - 1 for the horizontal shift:

Click "Show Answer" to reveal the answer and analysis