Math Problem Statement

Determine the domain and the range of the relation, and tell whether the relation is a function: {(3,1), (28, -9), (44,1), (3,2), (60,2)}

Solution

Let's solve the problem step-by-step.

We have the relation defined by the following set of ordered pairs: {(3,1),(28,9),(44,1),(3,2),(60,2)}\{(3, 1), (28, -9), (44, 1), (3, 2), (60, 2)\}

  1. Domain of the Relation:
    The domain is the set of all the first elements (x-values) of the ordered pairs.

    From the given pairs:

    • The x-values are: 3,28,44,3,603, 28, 44, 3, 60

    Since we only list each value once, the domain is: {3,28,44,60}\{3, 28, 44, 60\}

  2. Range of the Relation:
    The range is the set of all the second elements (y-values) of the ordered pairs.

    From the given pairs:

    • The y-values are: 1,9,1,2,21, -9, 1, 2, 2

    After removing duplicates, the range is: {1,9,2}\{1, -9, 2\}

  3. Is the Relation a Function?
    To determine if the relation is a function, each input (x-value) must map to exactly one output (y-value). If an x-value maps to more than one y-value, it is not a function.

    In this relation:

    • The x-value 33 maps to both 11 and 22.

    Since 33 has two different outputs, this means the relation is not a function.

Summary:

  • Domain: {3,28,44,60}\{3, 28, 44, 60\}
  • Range: {1,9,2}\{1, -9, 2\}
  • Is it a Function?: No, it is not a function.

Would you like more details on any part of the solution? Here are some related questions you might find interesting:

  1. What is the difference between a relation and a function?
  2. How do you determine the domain and range from a graph?
  3. Can a function have repeated y-values?
  4. What makes a relation a one-to-one function?
  5. How can you represent a function using a table?

Tip: Always remember that for a relation to be a function, each input must have exactly one output—this is the key defining property of functions.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Relations
Functions
Domain
Range

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9