# Lesson 9

Increasing and Decreasing Functions

These materials, when encountered before Algebra 1, Unit 4, Lesson 9 support success in that lesson.

### Lesson Narrative

In this lesson, students write descriptions for situations that could be represented by given graphs, then draw graphs for given descriptions. The mathematical focus of the lesson is recognizing what is happening in a situation when functions increase or decrease so that students can refer to these situations in future lessons. In the associated Algebra 1 lesson, students compare two functions using the average rate of change and function values. Students are supported by examining simpler functions to recognize when they are increasing and decreasing, as well as looking at different graphs based on the same descriptions to compare the results and recognize some aspects that must be true.

Students model with mathematics (MP4) when they think of realistic values for populations of cities, towns, and villages that have given properties. Attention to precision (MP6) is also essential when recognizing features of those graphs that must be present and features that could be open to interpretation.

### Learning Goals

Teacher Facing

• Interpret the meaning of increase and decrease using graphs and situations.

### Student Facing

• Let’s look at what a graph does based on a situation.

Building Towards