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Understanding Domain and Range in Relations: Notation Techniques and Exercises

This lesson focuses on the concepts of domain and range in mathematical relations. Students will learn to express these concepts using various notation methods including set notation, interval notation, number line notation, and inequalities. The session will involve practical exercises where learners will match relations to their respective domains and ranges, and express them through different notational systems. By the end, students will understand how to identify permissible values for independent and dependent variables and gain insights into continuous and discrete data contexts.

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Understanding Domain and Range in Relations: Notation Techniques and Exercises

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  1. Pre Calculus 10 Lesson Domain and Range: Let’s use proper notation

  2. State the Domain and Range

  3. Ways to write this: the old way

  4. Interpret the meaning Let’s begin to use the Set Notation (curly brackets are used for this, or if there is no restriction on the domain or range we simply say x and read “x belongs to all real numbers” or “the domain is all real numbers).

  5. Task: Match each relation with its domain and range Identify what type of notation is being used to describe domain and range: words, inequalities, interval notation, number line, set notation. Choose one of the relations and express its domain and range using as many notation as you can (words, inequalities, interval notation, number line, set notation)

  6. Your turn to play #1 Express the domain (all permissible values of independent variable) and range (all permissible values of dependent variable) using the SET NOTATION.

  7. Your turn to play #2 Express the domain (all permissible values of independent variable) and range (all permissible values of dependent variable) using the INTERVAL NOTATION.

  8. Your turn to play #3 Express the domain (all permissible values of independent variable) and range (all permissible values of dependent variable) using the NUMBER LINE NOTATION.

  9. Your turn to play #4 Express the domain (all permissible values of independent variable) and range (all permissible values of dependent variable) using the INEQUALITIES NOTATION.

  10. Your turn to play #5 Express the domain (all permissible values of independent variable) and range (all permissible values of dependent variable) using the INEQUALITIES NOTATION.

  11. Your turn to play #6 Express the domain (all permissible values of independent variable) and range (all permissible values of dependent variable) using the NUMBER LINES NOTATION Note: This relation has a non permissible value.

  12. So far, all the relations involved CONTINUOUS DATA. We could have DISCRETE DATA too. In such case it is best to use SET NOTATION to describe domain and range (permissible values of input and output variables) Give some examples of CONTINUOUS quantities and some examples of DISCRETE quantities.

  13. Your turn to play #7

  14. Given a function, there could be a need to set the domain arbitrarily (based on the context)

  15. Graph for each of the specified domains.

  16. Solution

  17. Your turn to play

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