In this lesson, students deepen their understanding of functions by comparing representations of several functions relating the same pair of quantities. They analyze two or more graphs simultaneously, interpreting their relative features and their average rates of change in context.

Students also study comparative statements in function notation, such as or , and explain them in terms of changes in population, changes in the trends of phone ownership, and the popularity of different television shows. Particular attention is given to any intersection points between graphs as places where two functions share an output value for the same input value.

Making comparisons involves looking beyond individual pieces of information. To accurately relate the information from multiple representations requires careful and precise use of mathematical language and notation (MP6). Students continue reasoning abstractly and quantitatively (MP2) as they use their analyses of representations of functions to draw conclusions about the quantities in situations.