7. Which relation is a function? \( \begin{array}{l}\text { (O) A. }(2,7),(6,5),(4,4),(3,3),(2,1) \\ \text { O B. }(1,1),(2,2),(3,3),(4,4),(5,8) \\ \text { O C. }(9,-2),(9,3),(4,-2),(4,2),(0,0) \\ \text { O D. }(1,0),(3,0),(1,1),(3,1),(1,3)\end{array} \)

A function is a special type of relation where each input (or x-value) corresponds to exactly one output (or y-value). In the options given, both A and B are functions because no x-value repeats. However, options C and D fail the test: they have repeated x-values with different corresponding y-values, making them not functions. So, in this case, A and B are the winners! One fun fact about functions is that the concept dates back to the works of mathematicians like René Descartes and Leonhard Euler in the 17th and 18th centuries. They laid the groundwork for the formal definitions we use today, demonstrating how functions could be represented graphically and algebraically — a pivotal moment that transformed modern mathematics. For anyone looking to dive deeper into this topic, there’s a wealth of resources available! Check out “The Art of Problem Solving: Precalculus” by Richard Rusczyk for a playful approach to understanding functions. Online platforms like Khan Academy also offer engaging videos and exercises that can reinforce these concepts in a fun and interactive way!