Algebra-2

To find the equation for the function based on the given properties, we need to analyze the transformations applied to the original function .

 

1.Horizontal Shift: The function approaches as x approaches 5 from the left and as x approaches 5 from the right. This suggests a vertical asymptote at x = 5, indicating a horizontal shift to the right. Therefore, we would replace x with x - 5.

 

2.Vertical Shift: The horizontal asymptote of the transformed function approaches -1 as x approaches . This suggests a vertical shift downward. To achieve this, we would subtract 1 from the function.

 

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

Replace x with x - 5 for the horizontal shift:

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