Lesson objective: Solve a real-life problem by comparing behaviors of functions.

This lesson provides an opportunity for students to apply their knowledge and understanding of function behaviors to a real-life situation. Students are asked to decide which pool fills at a faster rate, which fills first, and who pays more to fill their pool.

Key Concept students will use:

- Graphing inputs and outputs as ordered pairs, or looking at the graphs of functional relationships, allows us to compare the behaviors of functions qualitatively.

Skills students will use:

- Compare the behavior of two functions represented as graphs.
- Create the graphs of functions based on the description of the behavior of those functions.
- Answer questions to compare the functions.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) and Mathematical Practice 4 (model with mathematics) as they analyze the behavior of functions and create the models of functions.

**Key vocabulary: **

- behavior
- compare
- constant
- decreasing
- function
- increasing