Complete the relation so that it is a function. Explain your reasoning.   (-6,-1) , (-4,0) , (-2,1) , (2,2) (response)

To complete the relation so that it is a function, we need to ensure that each input (or domain value) is paired with exactly one output (or range value). A relation is a function if no two ordered pairs have the same first element (input) and different second elements (outputs).

The given set of points is:

\[
(-6, -1), (-4, 0), (-2, 1), (2, 2)
\]

### Step-by-Step Reasoning:

- A function has one unique output for each input.
- We check the first elements (inputs): \(-6, -4, -2, 2\).
- All these values are distinct, meaning no input is repeated.

Since there are no repeated inputs in the current set, the relation already satisfies the definition of a function. Therefore, **no additional points are needed to complete the relation as a function**.

### Conclusion:

The relation \(\{(-6, -1), (-4, 0), (-2, 1), (2, 2)\}\) is already a function because each input corresponds to exactly one output, and no input is associated with multiple outputs.

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Do you want more details or have any questions?

Here are 5 related questions:
1. What happens if an input is repeated with a different output?
2. How can you tell graphically if a relation is a function?
3. Can a relation with repeated outputs still be a function?
4. What is the difference between a relation and a function?
5. Can a vertical line intersect a graph of a function more than once?

**Tip**: In a function, you can always use the **vertical line test**—if a vertical line intersects the graph more than once, it’s not a function.

Complete the relation so that it is a function. Explain your reasoning. (-6,-1) , (-4,0) , (-2,1) , (2,2)

Learn how to determine if a relation is a function by examining input-output pairs. This step-by-step solution explains the criteria for a relation to be classified as a function using the example set of points (-6,-1), (-4,0), (-2,1), (2,2). Suitable for students in Grades 8-10.

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