In this lesson, students build toward describing the effects of a transformation on the equation of a function, without using a graph. Students begin with both a graph and equation of a function which has already undergone a transformation and consider what transformations would be needed to return the graph to its original form. 

Then, students sort graphs and equations of functions with a focus on recognizing the transformation in each representation. As students compare transformations in both the equations and graphs, they examine the structure of the equations of transformed functions (MP7).

Finally, students write equations for multiple types of functions that have undergone the same transformation and compare the equations. This gives students an opportunity to leverage repeated reasoning as they generalize an equation for an unknown function that has undergone the same transformation (MP8).