A calculus of the absurd
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4.7 Transformations of functions
4.7.1 Y-axis transformations
These are the easier case (at least in my view) to think about. When transforming a function \(f(x)\) in the y-axis, there are two key transformations to be aware of - stretching and translating.
To translate a function in the y-axis we can just add something to it, e.g. to shift the graph of \(y=f(x)\) three units up, define a variable, e.g. \(Q=f(x)+3\) - the 2D graph of this function will then be shifted three units above. This is illustrated on the graph below:
