We again
factor the middle in order to resolve the sequence of transformations. 1.5 f (3x6) +5 = 1.5 f [ 3(x2) ] + 5 This means that the first transformation is of x2. This results in shifting the graph right 2 units. 

The second
transformation involved the 3 coefficient inside the function. This
results in a horizontal compression of 3 factors. The result should look
like something on the right.


The third transformation is a constant scalar that lies outside of the function. We multiply all the y values by 1.5 to get the new function shape.  
The last
transformation comes from the + 5 that lies outside of the function. We
add 5 to all the y values of the function, which is the same as shifting
up the graph 5 units. Many of the data points have left this graph's viewable region, so it may be difficult to tell the exact values of the graph currently. 

This is a
comparison between the original function and the new function. In this
example, we use all four standard transformations. These are the core tools that you'll need to understand basic function manipulation. 