Dilatasi Vertikal Hal 27-29 Bab 1 TRANSFORMASI FUNGSI Kelas 12 SMA SMK Kurikulum Merdeka

Introduction

This tutorial focuses on vertical dilation, a key concept in the transformation of functions for students in Kelas 12 SMA/SMK under the Kurikulum Merdeka. Understanding vertical dilation helps students manipulate and analyze functions effectively, which is essential for advanced mathematics studies.

Step 1: Understanding Vertical Dilation

Vertical dilation involves stretching or compressing a function graphically along the vertical axis. This transformation affects the output values of the function without changing the input values.

• Vertical dilation is represented mathematically as:
  • y = k * f(x)
  • Where:
    • f(x) is the original function
    • k is the dilation factor
      • If k > 1, the graph stretches vertically.
      • If 0 < k < 1, the graph compresses vertically.

Practical Tip

When determining the value of k, consider the effect on the function's maximum and minimum values. For instance, if you have a function with a maximum of 5, and you apply a dilation factor of 2, the new maximum will be 10.

Step 2: Applying Vertical Dilation

To apply vertical dilation to a given function, follow these steps:

1. Identify the original function f(x).
2. Decide on the dilation factor k.
3. Write the new function using the dilation formula:
   • New function: y = k * f(x)
4. Graph the original function and the new function on the same set of axes.

Example

• Original function: f(x) = x^2
• Dilation factor: k = 3
• New function: y = 3 * x^2

Common Pitfall

Be cautious with the dilation factor. Remember that a negative k value will reflect the graph across the x-axis, which may not be the intended transformation.

Step 3: Analyzing the Effects

After applying vertical dilation, analyze how the transformation changes the properties of the function:

• Check for changes in:
  • Vertex position (for quadratic functions)
  • Intercepts (x-intercepts and y-intercepts)
  • Overall shape and direction of the graph

Real-World Application

Understanding vertical dilation can be useful in various fields such as physics, engineering, and economics, where modeling relationships and trends is essential.

Conclusion

Vertical dilation is a fundamental transformation that alters the vertical stretch of functions. By practicing the application and analysis of these transformations, students will enhance their understanding of function behavior. As a next step, explore horizontal dilation and other transformations to broaden your grasp of function manipulations. For further learning, consider reviewing related videos on horizontal dilation and combined transformations.