Graphing Domain and Range: Mastering Interval Notation

PreAlgebra Grades High School 5:53 Video
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Lesson Description

Learn to identify and express the domain and range of functions from their graphs using interval notation. This lesson covers key concepts with examples and practice problems.

Video Resource

Finding the Domain and Range From a Graph (Interval Notation)

Mario's Math Tutoring

Duration: 5:53
Watch on YouTube

Key Concepts

  • Domain of a function
  • Range of a function
  • Interval notation
  • Graphical representation of functions

Learning Objectives

  • Define domain and range of a function.
  • Identify the domain and range of a function from its graph.
  • Express the domain and range using interval notation.

Educator Instructions

  • Introduction (5 mins)
    Begin by defining the domain and range of a function. Explain that the domain represents all possible input values (x-values), and the range represents all possible output values (y-values). Briefly introduce interval notation as a way to express these sets of values.
  • Video Presentation (15 mins)
    Play the YouTube video 'Finding the Domain and Range From a Graph (Interval Notation)' by Mario's Math Tutoring. Encourage students to take notes on the examples provided in the video. Instruct them to pay close attention to how the domain and range are determined from the graphs and how they are written in interval notation.
  • Guided Practice (15 mins)
    Work through the examples from the video as a class. Pause at each example and ask students to predict the domain and range. Discuss the reasoning behind each answer, emphasizing the importance of scanning the graph horizontally (for domain) and vertically (for range). Review the correct use of parentheses and brackets in interval notation.
  • Independent Practice (10 mins)
    Present students with new graphs and have them determine the domain and range in interval notation independently. Circulate to provide assistance as needed.
  • Wrap-up and Discussion (5 mins)
    Review the key concepts and address any remaining questions. Discuss common mistakes and strategies for avoiding them.

Interactive Exercises

  • Graph Matching
    Provide students with a set of graphs and a corresponding set of domain and range written in interval notation. Have them match each graph with its correct domain and range.
  • Error Analysis
    Present students with examples of incorrectly identified domain and range in interval notation. Have them identify the errors and correct them.

Discussion Questions

  • What does a parenthesis in interval notation signify?
  • What does a bracket in interval notation signify?
  • How do you represent all real numbers in interval notation?
  • What strategies can you use to avoid common errors when identifying domain and range from a graph?

Skills Developed

  • Visual analysis of graphs
  • Understanding of function behavior
  • Application of interval notation
  • Problem-solving

Multiple Choice Questions

Question 1:

What does the domain of a function represent?

Correct Answer: All possible input values

Question 2:

What does the range of a function represent?

Correct Answer: All possible output values

Question 3:

Which of the following is the correct interval notation for all real numbers?

Correct Answer: (-∞, ∞)

Question 4:

What does a parenthesis '(' or ')' in interval notation indicate?

Correct Answer: The endpoint is not included

Question 5:

What does a bracket '[' or ']' in interval notation indicate?

Correct Answer: The endpoint is included

Question 6:

If a graph extends infinitely to the left, what is the lower bound of its domain?

Correct Answer: -∞

Question 7:

If a graph extends infinitely upwards, what is the upper bound of its range?

Correct Answer: ∞

Question 8:

The domain of a function is (-∞, 5]. Does the graph include the value x = 5?

Correct Answer: Yes

Question 9:

The range of a function is [2, ∞). Does the graph include the value y = 2?

Correct Answer: Yes

Question 10:

Which of the following represents a function with a domain restricted to x > 3?

Correct Answer: (3, ∞)

Fill in the Blank Questions

Question 1:

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

Correct Answer: domain

Question 2:

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

Correct Answer: range

Question 3:

________ notation is used to express the domain and range as intervals of numbers.

Correct Answer: Interval

Question 4:

A ________ indicates that an endpoint is included in the interval.

Correct Answer: bracket

Question 5:

A ________ indicates that an endpoint is not included in the interval.

Correct Answer: parenthesis

Question 6:

The symbol ________ represents positive infinity.

Correct Answer: ∞

Question 7:

The symbol ________ represents negative infinity.

Correct Answer: -∞

Question 8:

If a function's graph shows a hole at x = 2, then 2 is ________ from the domain.

Correct Answer: excluded

Question 9:

The domain of a function graphed as a horizontal line is ________.

Correct Answer: (-∞, ∞)

Question 10:

The range of a function graphed as a horizontal line is ________.

Correct Answer: a single value

Educational Standards

PC.F.1.1:Interpret characteristics of a function defined by an expression in the context of the situation. PC.F.1.3:Interpret characteristics of graphs and tables for a function that models a relationship between two quantities in terms of the quantities. PC.F.1.4:Describe end behavior, asymptotic behavior, and points of discontinuity.

Teaching Materials

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