Relasi Dan Fungsi (2) | Konsep Pemetaan | Domain, Kodomain, Range

Introduction

In this tutorial, we will explore the concepts of relations and functions as presented in the video "Relasi Dan Fungsi (2) | Konsep Pemetaan | Domain, Kodomain, Dan Range". Understanding these mathematical concepts is crucial for Grade 8 students as they form the foundation for more advanced topics in mathematics. We will cover the definitions of functions, domain, codomain, and range, along with practical examples.

Step 1: Understanding Functions

• A function is a special type of relation where each input (from the domain) is associated with exactly one output (in the codomain).
• To identify a function, check if any input has multiple outputs. If it does, it is not a function.

Practical Tips

• You can represent functions using mappings, tables, or graphs.
• Always visualize the relationship to better understand how inputs relate to outputs.

Step 2: Defining Domain

• The domain of a function is the set of all possible input values (x-values) that the function can accept.
• To determine the domain, consider:
  • Any restrictions on the input values (e.g., cannot divide by zero).
  • The context of the problem (e.g., negative values might not make sense in certain situations).

Example

For the function f(x) = 1/x, the domain is all real numbers except x = 0.

Step 3: Understanding Codomain

• The codomain is the set of all possible output values (y-values) of a function.
• It is important to note that the codomain includes all values that could possibly be output, even if they are not actually reached by the function.

Key Points

• The codomain can be specified explicitly (for instance, all real numbers) or can be inferred from the context of the problem.

Step 4: Identifying Range

• The range of a function is the actual set of output values produced by the function from the domain.
• To find the range, evaluate the function for all values in the domain and list the outputs.

Steps to Determine Range

1. Identify the domain of the function.
2. Calculate the output for each input.
3. Collect all unique output values to form the range.

Example

For f(x) = x^2, if the domain is all real numbers, the range is all non-negative real numbers (y ≥ 0).

Conclusion

In this tutorial, we covered the fundamental concepts of functions, domain, codomain, and range. Understanding these terms is essential for further studies in mathematics. As a next step, practice identifying the domain, codomain, and range for various functions to solidify your understanding. For additional resources, refer to the recommended playlists linked in the video description. Happy learning!