Relasi & Fungsi (1) - Relasi, Pengertian Relasi, Contoh Relasi - Matematika SMP

Introduction

This tutorial provides an overview of relations and functions in mathematics, aimed at middle school students. It will cover definitions, types of relations, and various ways to express and transform them, making it easier to understand these concepts.

Step 1: Understand Types of Functions

• Familiarize yourself with different types of functions, which include:
  • One-to-One Function: Each element of the domain maps to a unique element in the codomain.
  • Onto Function: Every element of the codomain is mapped by at least one element of the domain.
  • Many-to-One Function: Multiple elements of the domain can map to the same element in the codomain.

Step 2: Expressing Relations and Functions

• Learn how to express relations and functions using different notations:
  • Set Notation: Use sets to define relations, for example, R = {(x, y) | x is related to y}.
  • Arrow Diagrams: Visual representation where elements from the domain point to their corresponding codomain elements.
  • Graphs: Plotting points on a Cartesian plane to show relationships between variables.

Step 3: Identify Domain, Codomain, and Range

• Domain: The set of all possible input values for a function.
• Codomain: The set of potential output values, which may include values that are not the actual output.
• Range: The actual set of output values produced by the function.

Step 4: Transforming Relations from Arrow Diagrams

• To convert an arrow diagram into a set of ordered pairs:
  • Identify each element in the domain.
  • Match them with corresponding elements in the codomain.
  • Write these pairs in the format (domain element, codomain element).

Step 5: Expressing Relations in Three Forms

• A relation can be represented in three forms:
  • Set of Ordered Pairs: For example, R = {(1,2), (2,3), (3,4)}.
  • Arrow Diagrams: Draw arrows connecting elements of the domain to the codomain.
  • Graph: Plot the ordered pairs on a graph to visualize the relation.

Step 6: Converting from Graphs

• To convert a graph into a set of ordered pairs:
  • Identify key points on the graph.
  • Record their coordinates as (x, y) pairs.
  • Ensure that each point represents a unique relation.

Step 7: Working with Ordered Pair Sets

• Given a set of ordered pairs, determine the relation:
  • List all unique input values (domain) and output values (codomain).
  • Check for one-to-one or many-to-one relationships based on the pairs.

Step 8: Analyzing Relations

• Determine the type of relation formed:
  • Check if each input has a unique output (one-to-one).
  • Identify if multiple inputs map to the same output (many-to-one).

Conclusion

In this guide, we explored the fundamental concepts of relations and functions, focusing on their definitions, types, and representations. Understanding these concepts is crucial for further studies in mathematics. For next steps, practice identifying and expressing relations from different representations to reinforce your learning.