State the range of the following relation. {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}Group of answer choicesno{–3, –1, 3, 6,6}{–3, –1, 6, 3, 6}{–3, –1, 3, 6}

Break Down the Problem

1. Identify the Relation: The relation is provided as a set of ordered pairs: {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}.
2. Determine the Range: The range of a relation consists of all the unique second elements (y-values) from the ordered pairs.

Relevant Concepts

1. Definition of Range: In the context of a relation, the range is the set of all output values (y-values) corresponding to the input values (x-values).

Analysis and Detail

1. Extract y-values: From the ordered pairs, we extract the second elements:
   • (2, –3) → y = –3
   • (4, 6) → y = 6
   • (3, –1) → y = –1
   • (6, 6) → y = 6
   • (2, 3) → y = 3
2. List Unique y-values: Now, we will compile the unique y-values:
   • From the pairs listed, we have –3, 6, –1, and 3. The value 6 appears twice but only counts once for the range.

Verify and Summarize

1. Unique Values Summary: The unique y-values extracted are: {–3, 6, –1, 3}.
2. Final List: The range is thus the unique set of these values.

Final Answer

The range of the relation is {–3, –1, 3, 6}.