Describe qualitatively the functional relationship between two quantities by analyzing a graph

What you'll learn

1. Describe a graph in qualitative terms by identifying where a function is increasing, decreasing, or constant, without computing exact values
2. Classify sections of a graph as linear (straight) or nonlinear (curved), and explain what each shape implies about the rate of change
3. Identify and describe key features of a graph -- where the function starts, where it reaches a maximum or minimum, where it ends, and where its behavior changes
4. Sketch a graph that matches a verbal description of a real-world situation, including the correct qualitative shape (increasing/decreasing, linear/nonlinear, constant segments)
5. Write a complete verbal "graph story" that accounts for every section of a given graph, using language such as "increases quickly," "stays constant," "decreases slowly," and "curves upward"

Prerequisites

• Understand that a function is a rule that assigns to each input exactly one output