Algebra-2

To find the equation of the function based on the provided properties, 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, suggesting a horizontal shift to the right. Thus, we replace x with x - 1.

 

2.Horizontal Asymptote: The graph approaches 3 as x approaches . This means there is a vertical shift upward, so we add 3 to the function.

 

Combining these transformations, we start with :

Replace x with x - 1 for the horizontal shift:

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