This lesson introduces students to inverse functions. The idea is developed through several contextual problems that each requires reversing a process and using outputs as inputs.

In the Warm-up and the first activity, students encounter the idea of inverse functions as they use Caesar shift ciphers to encode and decode messages. In such ciphers, encoding involves shifting the position of a letter in the alphabet a certain distance and in a certain direction. Decoding then means undoing, or reversing, the action.

In the second activity, students solve problems about currency exchange. They convert an amount in one currency (dollars) to another (pesos) and work with inverse functions as they do the opposite conversion (from pesos to dollars).

Throughout the lesson, students reason repeatedly with linear functions, working forward and backward as they perform calculations with numerical values. They practice finding regularity through repeated reasoning, which they then apply to write expressions or equations to describe inverse functions (MP8). Students continue to use multiple representations of functions and to make connections between them. In doing so, they make sense of quantities and relationships in concrete and abstract terms (MP2).