Pembahasan Asesmen 1 LKS Halaman 7 Nomor 1-5, Pengertian Fungsi - SMA Kelas XI Kurikulum Merdeka

Introduction

This tutorial provides a comprehensive guide to understanding the assessment questions from the mathematics curriculum for 11th grade, specifically focusing on functions and their compositions. We will discuss key concepts and provide step-by-step solutions to questions 1-5 from the assessment worksheet, which are essential for mastering the topic.

Step 1: Understand the Definition of a Function

• A function is a relation where each input is associated with exactly one output.
• Key terms to know:
  • Domain: The set of all possible input values.
  • Codomain: The set of potential output values.
  • Range: The actual set of output values produced by the function.

Practical Tips

• Always determine the domain and range of a function before starting to solve problems.
• Use function notation (f(x)) to represent functions clearly.

Step 2: Analyze Assessment Questions

Question 1

• Identify the function given in the problem.
• Determine its domain and range.
• Check if the function meets the definition (one output for each input).

Question 2

• Examine if the function is one-to-one (no two inputs have the same output).
• If applicable, identify the inverse function and its domain.

Question 3

• Look for composition of functions in the question.
• Recall that the composition of functions f(g(x)) means applying g first, then f.

Question 4

• Assess whether the given function is linear or non-linear.
• Discuss how the graph of the function would look based on its equation.

Question 5

• Solve for specific values of x using the function.
• Use substitution to find outputs for provided inputs.

Step 3: Solve Example Problems

Example for Question 1

• Given f(x) = 2x + 3:
  • Domain: All real numbers.
  • Range: All real numbers (since it’s a linear function).

Example for Question 2

• For f(x) = x^2:
  • Domain: All real numbers.
  • Range: All non-negative numbers (outputs are never negative).

Example for Composition (Question 3)

• If f(x) = x + 2 and g(x) = x^2, then:
  • The composition f(g(x)) = f(x^2) = x^2 + 2.

Conclusion

Understanding functions, their domains, ranges, and compositions is crucial for solving mathematical problems in the 11th grade curriculum. By following the steps outlined above and practicing with the assessment questions, you can build a strong foundation in these concepts. For further study, consider exploring more complex functions and their applications in real-world scenarios.