Students engage with the process of graphing functions and relations to gain a visual understanding of mathematical relationships. This involves plotting various function types—linear, quadratic, polynomial, and trigonometric—on coordinate planes. By examining how the graphs change with different equation parameters, students learn to predict and analyze the behavior of functions, enhancing their problem-solving skills in both theoretical and applied mathematics.

Functions and relations describe the connections between sets of numbers or variables. Students explore the concept of a function as a specific type of relation where each input is connected to exactly one output. They also study more general relations that might associate an input with multiple outputs. Understanding these mathematical structures is crucial for navigating more advanced topics in calculus, algebra, and beyond, providing the tools needed to tackle complex mathematical scenarios.

Students discover the practical applications of functions and relations in diverse fields such as economics, where functions model financial growth and consumer behavior; physics, where they describe trajectories and forces; and computer science, where functions are essential in coding and algorithm development. Understanding these applications demonstrates the ubiquity and importance of mathematical functions and relations in solving real-world problems and advancing technological innovation.