Unit 34: Functions and Representations

Day 7 of 30

Is it a function? Vertical line test

6-8Mathematics

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Learning Objective

Students will explore is it a function? vertical line test through guided practice and application.

Today's Lesson

In this lesson, we'll explore is it a function? vertical line test. Mathematical thinking develops logical reasoning and problem-solving abilities.

A function is a relationship where each input has exactly one output. Think of it as a machine: you put in a value (input/x), it processes it with a rule, and gives back one result (output/y). Function notation: f(x) means "function f at x." For example, if f(x) = 2x + 3, then f(5) = 2(5) + 3 = 13. Functions model relationships in the world: temperature over time, cost based on quantity, distance from speed. Every function has a domain (allowed inputs) and range (possible outputs). Functions are fundamental to mathematics!

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 is it a function? vertical line test. 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 is it a function? vertical line test to novel situations.

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