Let's say you have 2 graphs, y = 1/x and y = 1/(x-1). You know that they both look similar; both are rectangular hyperbolas. But yet they are not exactly the same. In what ways (mathematically) are they different? Transformation is one way to explain it.

Essentially, transformation is is modifying of the shapes of graphs in accordance to changes in their equations. Transformations not only explain the relationship between graphs, but also that between equations. One example is the change of domain and range of a function due to a change in the original function.

Before embarking on this journey through the various transformations, we recommend going through our section of curve sketching, to better understand the shapes of the graphs we are going to explain, as these will not be repeated.