Transformation: A function represents a relationship between x and y as well as a relationship between symbolic and graphical representations. Functional reasoning in the context of transforming a function involves recognizing how changes to the parameters in the equation affect the graph of the function. In this video, the student reasons functionally about the shape of y = x2 and y = 2x2, recognizing the graphs are not static shapes, that they keep getting wider and “go on forever and ever.” When discussing the graph of y = 2x2 he describes that doubling the x2 term results in the y- values getting “bigger faster.” He then describes how scaling the function y = x2 by ½ results in the y-values getting “bigger slower.”