Translasi Vertikal Hal 1-13 Bab 1 TRANSFORMASI FUNGSI Kelas 12 SMA SMK Kurikulum Merdeka

Summary

This educational video script focuses on the concept of function transformation, specifically vertical translation, in the context of the Indonesian Merdeka curriculum for 12th-grade students. It explains the mathematical process of translating points on a graph by a certain distance, using the example of a linear function y = 2x being translated upwards to y = 2x + 3. The script also discusses the effects of vertical translation on the graph of quadratic functions and provides practical examples, such as modeling the growth of bacteria and the price change of masks during the COVID-19 pandemic. It concludes with exercises using GeoGebra to visualize the translations.

Takeaways

• 📚 The lesson focuses on vertical transformations of functions, specifically translations, as part of the 'Merdeka' curriculum for 12th-grade high school students.
• 🔍 Translation is defined as a transformation that moves points in a certain direction and distance, which can be represented as a shift in the x and y coordinates.
• 📈 In matrix form, the translation of a point (x, y) by (a, b) results in a new point (x', y') where x' = x + a and y' = y + b.
• 📉 For linear functions, a vertical shift upwards or downwards changes the equation by adding or subtracting the shift value to the original equation.
• 📊 The script provides examples of vertical shifts for linear functions, such as changing from y = 2x to y = 2x + 3 when shifted upwards by 3 units.
• 📐 The script explains how to determine whether a graph has shifted upwards or downwards by comparing the original and new equations of the functions.
• 📘 It also discusses the vertical translation of quadratic functions, using the example of y = x² + 1 being translated to y = x² - 2 by subtracting 3 from the original function.
• 📌 The script uses GeoGebra to illustrate the graphical representation of function translations, showing the shift of the graphs in the coordinate plane.
• 🔢 The lesson includes practical examples, such as modeling the growth of bacteria with the function y = 2^x and its translation to y = 2^x + 1 after treatment.
• 📝 The script provides step-by-step instructions on how to translate a given linear equation, like 8X - 4y + 16 = 0, by a certain amount and determine the new equation and graph.
• 🤔 The importance of critical thinking is emphasized through the script, encouraging students to observe and analyze changes in function graphs after translations.

Q & A

What is the main topic of the video script?

The main topic of the video script is the concept of function transformation, specifically focusing on vertical translations in the context of mathematical functions.

What is a translation in the context of mathematical functions?

A translation in the context of mathematical functions is a transformation that moves points in a certain direction and distance, also known as a shift.

How is a point translated in a function?

A point is translated by shifting it by a certain distance 'a' horizontally and 'b' vertically, resulting in a new point with coordinates (x', y') where x' = x + a and y' = y + b.

What is the effect of vertical translation on the equation of a linear function?

Vertical translation affects the constant term in the equation of a linear function. For example, if the original function is y = 2x and it is translated upwards by 3 units, the new equation becomes y = 2x + 3.

How does a positive vertical translation change the graph of a function?

A positive vertical translation moves the graph of a function upwards. For instance, translating y = 2x upwards by 5 units results in the graph of y = 2x + 5.

What happens to the graph of a function when it is translated vertically by a negative value?

When a function is translated vertically by a negative value, its graph moves downwards. For example, translating y = 2x by -3 units results in the graph of y = 2x - 3.

What is the relationship between the original function y = 2x + 4 and its translated version y = 2x + 6?

The translated version y = 2x + 6 is obtained by adding 2 to the original function y = 2x + 4, indicating a vertical translation upwards by 2 units.

How does the script explain the vertical translation of quadratic functions?

The script explains that a quadratic function, such as y = x^2 + 1, can be translated vertically by subtracting a value from it, resulting in a new function like y = x^2 - 2, which represents a downward shift by 3 units.

What is the significance of the term 'b' in the context of vertical translation of functions?

The term 'b' in the equation y = f(x) + b represents the vertical shift of the function. If 'b' is positive, the graph shifts upwards, and if 'b' is negative, the graph shifts downwards.

Can you provide an example from the script where a real-world scenario is modeled using vertical translation of functions?

Yes, the script provides an example of a real-world scenario where the growth of bacteria after treatment is modeled. The original model is y = 2^x, and after treatment, it becomes y = 2^x + 1, indicating a vertical translation upwards by 1 unit.

How does the script use the concept of vertical translation to solve a problem related to a mask offer during a pandemic?

The script models the increasing demand for masks during the COVID-19 pandemic with the linear equation 8x - 4y + 16 = 0. After 8 days, the model changes due to translation, resulting in the new equation y = 2x + 4 + 8, which represents a vertical translation upwards by 8 units.

What is the new equation obtained after translating the function y = x^2 - 2x - 8 by 4 units upwards?

After translating the function y = x^2 - 2x - 8 upwards by 4 units, the new equation becomes y' = x^2 - 2x - 4, which is the result of adding 4 to the original function.