Recognizing Linear, Quadratic, and Exponential Relationships

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11th GradeCollege Board Pre-AP Classroom50 min

Learning Objective

Students will identify and distinguish linear, quadratic, and exponential relationships using multiple representations (graphs, tables, equations, and verbal descriptions) by analyzing patterns of change.

Lesson Overview

Students progress from identifying function families by shape to distinguishing them by constant differences, constant second differences, and constant ratios in tables — ultimately applying these tools to real-world contexts and mixed representations.

Materials

Whiteboard and dry-erase markers (or large paper)
Pencils and notebook paper
Basic calculator

Scaffolded Task Progression

1Task 1

Three graphs are shown below. Label each graph as belonging to one of these families: Linear, Quadratic, or Exponential. Be ready to explain your reasoning in one sentence each.

[ Interactive graph / diagram, available in the full lesson ]

2Task 2

Match each equation to its function family. Write Linear, Quadratic, or Exponential next to each one. No graphing allowed — use the equation structure only.

1.

y = 3 x - 7

y = 2 (4)^{x}

y = - x^{2} + 5 x - 1

y = - 2 x + 9

y = 5 (0.8)^{x}

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