Math Problem Statement

Determine the codomain and range of the function f: A → B from the given mapping diagram.

Solution

The image shows a question asking to determine the codomain and range of a function f:ABf: A \to B, based on the mapping diagram provided.

Diagram Interpretation:

  • Set A contains elements: {1,2,3}\{1, 2, 3\}.
  • Set B contains elements: {a,b,c,d}\{a, b, c, d\}.
  • The mapping is as follows:
    • 11 maps to aa,
    • 22 maps to cc,
    • 33 maps to dd.

Solution:

  • Codomain of ff: The codomain of a function is the set of all possible outputs, which in this case is the entire set BB. Therefore, the codomain of ff is {a,b,c,d}\{a, b, c, d\}.

  • Range of ff: The range of a function is the set of actual outputs based on the given mapping. The elements in set BB that are actually mapped by elements in AA are {a,c,d}\{a, c, d\}. Thus, the range of ff is {a,c,d}\{a, c, d\}.

Final Answer:

  • Codomain: {a,b,c,d}\{a, b, c, d\}

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Math Problem Analysis

Mathematical Concepts

Functions
Mappings
Sets

Formulas

-

Theorems

Codomain and Range of a Function

Suitable Grade Level

Grades 9-11