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Transformations of functions - Does anybody use this method?

Suppose we have y = f(x) , with some sort of curve drawn and some coordinates marked on the curve.

And then we have to draw the graph of y = 4 - 12*f(x/2 - 3)

I've seen people get confused about how to transform one graph into another.

And get the transform going the wrong way.

What I do is write the first equation as OldY = f(OldX) as we want to transform an old graph into a new graph.

And then I write the equation for the new graph as NewY = 4 -12*f(NewX/2 -3)

What goes into the function must be the same to get the same points back out of the function, so we equate brackets.

So NewX/2 - 3 = Old X, so New X = 2*OldX + 6

When we do that, we can write NewY = 4 -12*f(OldX)

As f(OldX) = OldY, we can write that as NewY = 4 - 12*OldY

And then it is easy to transform any point on the old graph into a point on the new graph.

With this method I just don't make mistakes about whether I should stretch or shrink one axis, or move the graph to the left or right.

Does anybody else use the Old graph, New Graph method?
I've never seen this method, but I can't see why it wouldn't work. I think most people would tend to just build the graph up in stages, though: apply the transformation in the order f(x) --> f(x/2) (stretch by 2) --> f(x/2 - 3) (translation by 3) --> -12f(x/2 - 3) (flip + stretch by 12) --> 4 - 12f(x/2 - 3) (translation by 4).
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stevencarrwork
OP
I think you are right. Most people would do it that way.

But I have seen people make mistakes that way, including myself.

I started making a lot fewer mistakes when I started labelling the x and Y with New or Old.

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