5. Consider the set of ordered pairs shown. $$ \{(-19,20),(-5,3),(19,82),(-20,2),(5,-5)\} $$ Which ordered pair, when added to the given set, will result in a function? $$ (19,24) $$ $$ (82,-5) $$ $$ (-5,5) $$ $$ (-20,4) $$

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To determine which ordered pair can be added to the given set while maintaining it as a function, we need to ensure that each input (the first element of the pair) maps to exactly one output (the second element of the pair).

The original set of ordered pairs is:
$$
\{(-19,20), (-5,3), (19,82), (-20,2), (5,-5)\}
$$
The first components (inputs) in this set are: $$-19, -5, 19, -20, 5$$.

Let's evaluate each option:

1. **$$(19, 24)$$**:
   - The input **19** already exists in the set with the output **82**.
   - Adding $$(19, 24)$$ would mean the input **19** maps to two different outputs (**82** and **24**), which violates the definition of a function.

2. **$$(82, -5)$$**:
   - The input **82** does not exist in the current set.
   - Adding $$(82, -5)$$ introduces a new input with a unique output.
   - This maintains the function property.

3. **$$(-5, 5)$$**:
   - The input **-5** already exists in the set with the output **3**.
   - Adding $$(-5, 5)$$ would mean the input **-5** maps to two different outputs (**3** and **5**), violating the function definition.

4. **$$(-20, 4)$$**:
   - The input **-20** already exists in the set with the output **2**.
   - Adding $$(-20, 4)$$ would mean the input **-20** maps to two different outputs (**2** and **4**), again violating the function definition.

**Conclusion:** Only the ordered pair $$(82, -5)$$ can be added without violating the properties of a function.

**Answer:** $$ (82,\ -5) $$
The ordered pair $$(82, -5)$$ can be added to the set to maintain it as a function.

5. Consider the set of ordered pairs shown. \[ \{(-19,20),(-5,3),(19,82),(-20,2),(5,-5)\} \] Which ordered pair, when added to the given set, will result in a function? \( (19,24) \) \( (82,-5) \) \( (-5,5) \) \( (-20,4) \)

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