Unlocking Relations and Functions: Domain, Range, and Mapping

Algebra 2 Grades High School 12:37 Video
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Lesson Description

Explore the fundamental concepts of relations and functions, including domain, range, mapping diagrams, and determining if a relation is a function. Learn to represent relations graphically and identify functions using the vertical line test.

Video Resource

Introduction to Relations and Functions Algebra | Discrete

Kevinmathscience

Duration: 12:37
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Key Concepts

  • Relations and Functions
  • Domain and Range
  • Mapping Diagrams
  • Vertical Line Test

Learning Objectives

  • Define and identify relations and functions.
  • Determine the domain and range of a relation.
  • Represent a relation using a mapping diagram.
  • Graph a discrete relation on a coordinate plane.
  • Use the vertical line test to determine if a relation is a function.

Educator Instructions

  • Introduction (5 mins)
    Begin by defining relations and functions. Emphasize that a relation is simply a set of ordered pairs, while a function is a special type of relation where each input (x-value) has only one output (y-value). Briefly introduce the concepts of domain and range as the sets of all possible inputs and outputs, respectively.
  • Domain and Range (10 mins)
    Explain how to identify the domain and range from a given set of ordered pairs. Provide examples and guide students through the process of listing the domain and range, ensuring they understand to list each value only once, even if it repeats in the relation.
  • Mapping Diagrams (10 mins)
    Introduce mapping diagrams as a visual representation of relations. Demonstrate how to create a mapping diagram by representing the domain and range as separate sets and using arrows to show the mapping between x and y values. Emphasize that multiple arrows can point to the same y-value, but not from the same x-value for it to be a function.
  • Graphing Discrete Relations (10 mins)
    Review how to plot points on a coordinate plane. Guide students through graphing a given relation by plotting each ordered pair as a point. Explain that these graphs are discrete because they consist of individual, unconnected points.
  • Is it a Function? (10 mins)
    Introduce the vertical line test as a method for determining whether a graph represents a function. Explain that if any vertical line intersects the graph at more than one point, the relation is not a function. Reinforce the concept that for a relation to be a function, each x-value must have only one y-value.
  • Examples and Practice (10 mins)
    Work through additional examples, varying the representation of relations (ordered pairs, mapping diagrams, graphs). Have students practice identifying the domain and range and determining whether a relation is a function. Encourage them to explain their reasoning.
  • Conclusion (5 mins)
    Summarize the key concepts of relations, functions, domain, range, mapping diagrams, and the vertical line test. Emphasize the importance of understanding these concepts for further study in algebra and other areas of mathematics.

Interactive Exercises

  • Mapping Diagram Creation
    Provide students with sets of ordered pairs and have them create mapping diagrams to represent the relations.
  • Graphing and Vertical Line Test
    Provide students with different graphs (some functions, some not) and have them use the vertical line test to determine which are functions.

Discussion Questions

  • What is the difference between a relation and a function?
  • Can you give an example of a relation that is not a function?
  • How does a mapping diagram help you visualize a relation?
  • How can the vertical line test help you determine if a relation is a function?
  • Why is it important to understand the domain and range of a function?

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Visual Representation
  • Analytical Skills

Multiple Choice Questions

Question 1:

Which of the following is NOT a way to represent a relation?

Correct Answer: Vertical line test

Question 2:

The domain of a relation is the set of all:

Correct Answer: x-values

Question 3:

The range of a relation is the set of all:

Correct Answer: y-values

Question 4:

Which of the following relations is a function?

Correct Answer: {(1, 2), (2, 2), (3, 2)}

Question 5:

If a vertical line intersects a graph at more than one point, the relation is:

Correct Answer: not a function

Question 6:

In a mapping diagram, arrows show the relationship between:

Correct Answer: domain and range

Question 7:

What is the range of the relation {(2, 4), (3, 9), (4, 16)}?

Correct Answer: {4, 9, 16}

Question 8:

Which test determines if a graph represents a function?

Correct Answer: Vertical line test

Question 9:

If the x-values in a relation do not repeat, then the relation is:

Correct Answer: always a function

Question 10:

Why is it important to understand if a relation is also a function?

Correct Answer: Functions have specific properties and can be used to model real-world scenarios.

Fill in the Blank Questions

Question 1:

A set of ordered pairs is called a ________.

Correct Answer: relation

Question 2:

The set of all possible input values of a relation is called the ________.

Correct Answer: domain

Question 3:

The set of all possible output values of a relation is called the ________.

Correct Answer: range

Question 4:

A ________ diagram visually represents the mapping between the domain and range.

Correct Answer: mapping

Question 5:

A relation is a ________ if each x-value has only one y-value.

Correct Answer: function

Question 6:

The ________ line test is used to determine if a graph represents a function.

Correct Answer: vertical

Question 7:

If any vertical line intersects a graph at more than one point, the relation is ________ a function.

Correct Answer: not

Question 8:

In a mapping diagram, ________ originate from the domain and point to the range.

Correct Answer: arrows

Question 9:

The ________ value is the independent variable in a relation.

Correct Answer: x

Question 10:

In mathematical terms, a function is a description of ________ (how related quantities vary together)

Correct Answer: covariation

Educational Standards

A2.F.1.1:Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain. A2.F.1:Understand functions as descriptions of covariation (how related quantities vary together).

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