What are the transformations that will happen to 1/x to get 3/(x+2)?

To determine the transformations that will happen to the function 1/x to get 3/(x+2), we can break it down into a series of steps:

Step 1: Horizontal Transformation
The expression (x+2) inside the denominator of 3/(x+2) indicates a horizontal transformation. Specifically, the graph of the function will shift to the left by 2 units compared to the graph of 1/x.

Step 2: Vertical Transformation
The constant factor 3 outside the fraction indicates a vertical transformation. In this case, the graph of 1/x will be vertically stretched by a factor of 3. This means that every point on the graph will be stretched vertically: if a point was originally (x, y), it will now be (x, 3y).

To summarize, the transformations required to obtain 3/(x+2) from 1/x are:
1. Leftwards shift by 2 units.
2. Vertical stretching by a factor of 3.