A transformation is something that is done to a graph/function that causes it to change in some way. This topic is about the effects that changing a function has on its graph.
There are two types of transformation you must be familiar with: translations and reflections. Throughout this topic, we will use the notation f(x) to refer to a function and describe the changes that happen to it.
When a function/graph is translated, it is shifted – left/right, up/down, or some combination of the two. If we let f(x) be any function, then the two types of translation are:
– f(x) + a; in this case, the function adds the value of a on top of all of its outputs. This means that the y values on the graph (the outputs of the function) are all increased by a. As a result, the whole graph is translated by a in the positive y direction (up).
– f(x + a); in this case, a is added to each input before it is passed into the function. This means that in order to get the same output from f(x + a) as from f(x), the input needed is going to be smaller by a, therefore the x values on the graph (the inputs of the function) are all decreased by a. As a result, the whole graph is translated by a in the negative x direction (left).