Combining Graphing Transformations

In this lesson, we will learn about combining graphing transformations. This topic involves finding the correct order to apply transformations to go from the parent graph f(x) to the graph of g(x). For the vertical transformations, things are very straightforward. We simply follow the order of operations. We will find that we will do any vertical stretch/compression with any reflection across the x-axis before doing any vertical shift. For the horizontal transformations, things tend to become a bit confusing. Here we will first factor out the coefficient of x and then work in the reverse of the order of operations. This means we will first deal with any horizontal stretch/compression with any reflection across the y-axis before doing any horizontal shift.