# 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: