Determine whether the relation is a function. Give the domain and range for the relation. $$ \{(-4,-4),(-6,-6),(-1,-1),(8,8)\} $$ Does the given relation represent a function? Yes No

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UpStudy AI · Accepted Answer

Yes, the given relation represents a **function**.

### Explanation:

A **function** is a relation in which each input (first element of the ordered pair) is associated with exactly one output (second element of the ordered pair).

Let's examine the given relation:
$$
\{\, (-4, -4),\ (-6, -6),\ (-1, -1),\ (8, 8) \,\}
$$

- **Inputs (Domain Candidates):** -4, -6, -1, 8
- **Outputs (Range Candidates):** -4, -6, -1, 8

Each input is **unique** and maps to one output only:
- -4 maps to -4
- -6 maps to -6
- -1 maps to -1
- 8 maps to 8

Since there are no repeated inputs with different outputs, the relation satisfies the definition of a function.

### Domain and Range:

- **Domain:** $$\{-6,\ -4,\ -1,\ 8\}$$
  
  *(The set of all input values.)*

- **Range:** $$\{-6,\ -4,\ -1,\ 8\}$$
  
  *(The set of all output values.)*

### Conclusion:

- **Does the given relation represent a function?**  
  **Yes**
Yes, the relation is a function. The domain is $$\{-6, -4, -1, 8\}$$ and the range is $$\{-6, -4, -1, 8\}$$.

Determine whether the relation is a function. Give the domain and range for the relation. \( \{(-4,-4),(-6,-6),(-1,-1),(8,8)\} \) Does the given relation represent a function? Yes No

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