Unit 34: Functions and Representations

Day 26 of 30

Comparing linear and non-linear functions

6-8Mathematics

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Learning Objective

Students will compare linear and non-linear functions through guided practice and application.

Today's Lesson

In this lesson, we'll explore comparing linear and non-linear functions. Mathematical thinking develops logical reasoning and problem-solving abilities.

This concept is important because it builds upon what you've already learned and prepares you for more advanced topics. As you study this material, look for patterns, connections, and real-world examples that help make the concept concrete and memorable.

As you work through today's material, pay attention to the examples and try to identify the patterns or strategies being used. This will help you apply these concepts to new problems.

Take notes on key points and make connections to what you've already learned in previous lessons.

Key Terms
Problem

A mathematical question requiring analysis and solution

Solution

The result obtained by solving a problem

Activities
Instructions
1. Review the example problems for comparing linear and non-linear functions. 2. Identify the steps and strategies used. 3. Work through practice problems independently. 4. Compare solutions with a partner.
Materials Needed
  • Notebook
  • Calculator (if needed)
  • Graph paper
Practice Problems
1

If f(x) = 3x + 2, find f(4)

Hint: Substitute 4 for x.
2

Is the relation {(1,2), (2,3), (1,4)} a function?

Hint: Check if any x-value repeats with different y.
3

If f(x) = x² - 1, find f(-2)

Hint: Substitute -2 for x. Remember (-2)² = 4.

Teaching Tip

For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply comparing linear and non-linear functions to novel situations.

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