In this lesson, students compare two functions represented in different ways (graph and table, graph and equation, and, optionally, table and verbal description). In each case, students use the different representations to find outputs for different inputs. Even though they use different representations, students are looking for the same information about the contexts and need to interpret each representation appropriately (MP2).

In a graph, students identify the input on the horizontal axis, then find the corresponding coordinate point on the graph, which lets them read the associated output. In a table, they find the input value in the first row (or column) and read the output value in the second. For functions represented by equations, students substitute the input value into the expression on one side of the equation and compute the corresponding output value on the other. Students also look for inputs corresponding to a given output by trying to reverse these procedures.

Each representation has strengths and weaknesses. Comparing them in the Lesson Synthesis helps students make decisions about how to use these representations strategically in the future.

The last activity is optional. Consider using it if students would benefit from additional practice of comparing a function represented by words with one represented by a table.

Note that this lesson specifically avoids comparisons of linear functions to other linear functions in order to avoid students associating “function” with only linear relationships. In a later lesson, students revisit some of these ideas and compare linear functions.