Lesson objective: Understand that some functions are nonlinear.

Students bring prior knowledge of comparing the rate of change for linear equations from 8.F.A.2. This prior knowledge is extended to comparing rates of change for nonlinear functions as students use tables and graphs to compare pricing functions. A conceptual challenge students may encounter is that nonlinear functions look and behave differently than linear functions.

The concept is developed through work with tables and graphs, which give structure for comparing rates of change.

This work helps students deepen their understanding of equivalence, because functions can be represented in descriptions, tables and graphs.

Students engage in Mathematical Practice MP.2 (reason abstractly and quantitatively) as they analyze graphs of linear and nonlinear functions to find the lowest prices for shipping.

**Key vocabulary:**

- function
- nonlinear
- rates of change

**Special materials needed:**