# Multiple Transformation of Graphs

In the last post, we talk about single transformation of graphs. This could mean a single reflection, translation or scaling. However, in the A Level exam, we are going to do multiple transformations.

## Order of transformation

Whenever we are doing multiple transformation, it is recommended to follow this order:

1. Translate in x direction (Tx)
2. Scale/ reflect in x- direction (Sx)
3. Scale/ reflect in y- direction (Sy)
4. Translate in y direction (Ty)

Often, we abbreviate this order to Tx, Sx, Sy, Ty.

## Example of multiple transformation

Given y = f(x), describe the series of transformation needed to obtain y = 2f(3x+2)-5.

Solutions:

To sketch y = 2f(3x+2)-5, we should transform the graph of y = f(x) in this order:

Step 1: translate y = f(x) by -2 units in the x- direction to obtain y = f(x+2)

Step 2: Scale y= f(x+2) by a scale factor of 1/3 parallel to the x-axis to obtain y = f(3x+2)

Step 3: Scale y = f(3x+2) by a scale factor of 2 parallel to the y- axis to obtain y = 2f(3x+2)

Step 4: Translate y= 2f(3x+2) by -5 units in the y direction to obtain y = 2f(3x+2)-5

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