Pregunta
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Look at this set of ordered pairs: \[ \begin{array}{l}(-18,15) \\ (-17,3) \\ (5,3) \\ (6,-3) \\ (10,3)\end{array} \] Is this relation a function? yes no

Ask by Knight Savage. in the United States
Mar 19,2025

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Yes, the relation is a function.

Solución

1. A relation is a function if every input (first coordinate) has exactly one output (second coordinate). 2. The ordered pairs given are \(\{(-18, 15), (-17, 3), (5, 3), (6, -3), (10, 3)\}\). 3. List the \( x \)-coordinates (inputs): \(-18, -17, 5, 6, 10\). 4. Check if any \( x \)-coordinate appears more than once: - \(-18\) appears once. - \(-17\) appears once. - \(5\) appears once. - \(6\) appears once. - \(10\) appears once. 5. Since each \( x \)-coordinate is unique, the relation assigns exactly one output to each input. Therefore, the relation is a function.

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Bonus Knowledge

To determine if this relation is a function, we need to check if each input (the first number in each ordered pair) maps to exactly one output (the second number). In this case, the inputs are -18, -17, 5, 6, and 10, all of which map to unique outputs (15, 3, 3, -3, and 3 respectively). The input 5 has the same output as the input -17, but since each input has only one corresponding output and isn't repeated with a different partner, this relation satisfies the definition of a function. So, yes, this relation is a function! For more clarity, remember that functions can have the same output for different inputs. What matters is that each input only corresponds to one output. So while we see the output 3 showing up multiple times for different inputs, it doesn’t disqualify the relation from being a function. It still checks out!

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