Relations and Functions Overview
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Questions and Answers

What is the domain and range of the relation {(4, −2), (−1, 1), (2, −3), (3, 0)}?

Domain: {-1, 2, 3, 4}; Range: {-3, -2, 0, 1}

What is the domain and range of the relation {(3, 4), (1, −2), (4, −1), (2, 2)}?

Domain: {1, 2, 3, 4}; Range: {-2, -1, 2, 4}

What is the domain and range of the relation {(3, −4), (2, 0), (−4, −1), (0, −3)}?

Domain: {-4, 0, 2, 3}; Range: {-4, -3, -1, 0}

What is the domain and range of the relation {(3, 2), (-2, 4), (4, -4), (4, 0), (-1, -3)}?

<p>Domain: {-2, -1, 3, 4}; Range: {-4, -3, 0, 2, 4}</p> Signup and view all the answers

What is the domain and range of the relation {(-1, -5), (2, -3), (3, -2), (5, 1), (-4, 2)}?

<p>Domain: {-4, -1, 2, 3, 5}; Range: {-5, -3, -2, 1, 2}</p> Signup and view all the answers

Is the relation { (-1,2), (2, 51), (1, 3), (8, 22), (9, 51) } a function?

<p>True</p> Signup and view all the answers

Is the relation {(1, -2), (-2, 0), (-1, 2), (1, 3)} a function?

<p>False</p> Signup and view all the answers

Is the relation {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)} a function?

<p>True</p> Signup and view all the answers

Is the relation {(-2, -1), (0, 3), (5, 4), (-2, 3)} a function?

<p>False</p> Signup and view all the answers

Is the relation {(-1, 5), (0, 3), (2, 3), (3, -1)} a function?

<p>True</p> Signup and view all the answers

Is the relation {(-1, 7), (0, -3), (1, 10), (0, 7)} a function?

<p>False</p> Signup and view all the answers

Does the relation {(2, 4), (-8, 0), (1, 5), (3, 1)} represent a function?

<p>True</p> Signup and view all the answers

Study Notes

Relations and Functions Overview

  • Relations can be represented in various forms, including tables, graphs, and mappings.
  • A key aspect of relations is identifying the domain (set of x-values) and range (set of y-values).

Example Relations and Their Domains/Ranges

  • Relation: {(4, −2), (−1, 1), (2, −3), (3, 0)}

    • Domain: {-1, 2, 3, 4}
    • Range: {-3, -2, 0, 1}

  • Relation: {(3, 4), (1, −2), (4, −1), (2, 2)}

    • Domain: {1, 2, 3, 4}
    • Range: {-2, -1, 2, 4}

  • Relation: {(3, −4), (2, 0), (−4, −1), (0, −3)}

    • Domain: {-4, 0, 2, 3}
    • Range: {-4, -3, -1, 0}

  • Relation: {(3, 2), (−2, 4), (4, −4), (4, 0), (−1, −3)}

    • Domain: {-2, -1, 3, 4}
    • Range: {-4, -3, 0, 2, 4}

  • Relation: {(-1, -5), (2, -3), (3, -2), (5, 1), (-4, 2)}

    • Domain: {-4, -1, 2, 3, 5}
    • Range: {-5, -3, -2, 1, 2}

Function Determination

  • To qualify as a function, each x-value must correspond to exactly one y-value.

  • Example: { (-1, 2), (2, 51), (1, 3), (8, 22), (9, 51)}

    • Function: Yes
    • Domain: {-1, 2, 1, 8, 9}
    • Range: {2, 51, 3, 22}

  • Example: {(1, -2), (-2, 0), (-1, 2), (1, 3)}

    • Function: No (x=1 maps to -2 and 3)
    • Domain: {-2, -1, 1}
    • Range: {-2, 0, 2, 3}

  • Example: {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)}

    • Function: Yes
    • Domain: {1, 2, 3, 4, 5}
    • Range: {1, 2, 5, 10, 15}

Mappings and Functions

  • Mappings visually represent relations.

  • Example: {(-2, -1), (0, 3), (5, 4), (-2, 3)}

    • Function: No (x=-2 maps to -1 and 3)
    • Domain: {-2, 0, 5}
    • Range: {-1, 3, 4}

  • Example: {(-1, 5), (0, 3), (2, 3), (3, -1)}

    • Function: Yes
    • Domain: {-1, 0, 2, 3}
    • Range: {5, 3, -1}

  • Example: {(-1, 7), (0, -3), (1, 10), (0, 7)}

    • Function: No (x=0 maps to -3 and 7)
    • Domain: {-1, 0, 1}
    • Range: {-3, 7, 10}

Mapping Diagram

  • A mapping diagram illustrates the relationship between elements of the domain and range.
  • Example: {(2, 4), (-8, 0), (1, 5), (3, 1)}
    • Function: Yes (each x-value is unique)

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Description

This quiz covers the basics of relations and functions, including how to identify the domain and range of given relations. It includes examples of relations in different forms and explains the criteria for determining if a relation qualifies as a function. Test your understanding of these concepts with this informative quiz.

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