A calculus of the absurd

4.6 Transformations of functions

4.6.1 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:

(-tikz- diagram)