Refleksi Vertikal Hal 19-23 Bab 1 TRANSFORMASI FUNGSI Kelas 12 SMA SMK Kurikulum Merdeka

Introduction

This tutorial provides a step-by-step guide to understanding vertical reflection in functions as discussed in the video "Refleksi Vertikal Hal 19-23 Bab 1 TRANSFORMASI FUNGSI Kelas 12 SMA SMK Kurikulum Merdeka." This content is designed for 12th-grade students studying the transformation of functions in accordance with the Merdeka curriculum. Understanding vertical reflection is crucial for graphing functions and visualizing their transformations.

Step 1: Understanding Vertical Reflection

• Vertical reflection occurs when a function is mirrored across the x-axis.
• The general transformation can be represented as:
  • If f(x) is the original function, the reflected function is given by:

    f'(x) = -f(x) 
    

• This means that for every point (x, y) on the original graph, the corresponding point on the reflected graph will be (x, -y).

Step 2: Analyzing Graphical Changes

• When performing a vertical reflection:
  • Identify key points on the original function.
  • For each point (x, y), compute the new point:
    • New Point: (x, -y)
• Example:
  • If the original function has a point (2, 3):
    • The reflected point will be (2, -3).

Step 3: Sketching the Reflected Graph

• Follow these steps to sketch the reflected graph:
  1. Plot the original function.
  2. For each point on the original graph, plot the corresponding reflected point.
  3. Connect the reflected points to form the new graph.

Step 4: Exploring Real-World Applications

• Vertical reflection is used in various fields:
  • Physics: Analyzing wave functions.
  • Engineering: Understanding forces acting in opposite directions.
• Recognizing these applications aids in grasping the importance of function transformations.

Step 5: Practicing with Exercises

• Solve practice problems to reinforce your understanding:
  1. Given the function f(x) = x^2, reflect it vertically.
  2. Use critical points and intercepts to help sketch the reflected graph.
• Check your answers against the original function to ensure accuracy.

Conclusion

Vertical reflection is a fundamental concept in the transformation of functions, crucial for graphing and analysis. By understanding how to reflect functions, sketch their graphs, and apply these concepts to real-world situations, you can enhance your mathematical skills. For further practice, consider reviewing related topics like horizontal reflection and dilation in functions, as they build on this foundational knowledge.