MUDAH! Cara Menentukan Persamaan Awal Fungsi pada Transformasi TRANSFORMASI FUNGSI. Matematika Kl 12

Summary

This video lesson discusses how to determine the original equation of a function after various transformations such as translation, reflection, rotation, and dilation. The teacher explains that solving these problems requires reversing the transformation given in the question. For instance, translating with the opposite of the given vector, reflecting over the same axis or line, rotating by the opposite angle, or dilating by the reciprocal of the scale factor. Viewers are encouraged to refer to previous lessons for formulas and examples to reinforce their understanding.

Takeaways

• 📘 Transformations are categorized into four types: translation, reflection, rotation, and dilation.
• ✏️ To find the initial equation of a function after translation, apply the inverse of the given translation.
• 🔁 For reflection problems, use the same axis of reflection mentioned in the problem to find the original function.
• 🌀 When dealing with rotations, apply the inverse angle of rotation to determine the original function.
• 🔍 In dilation problems, the scale factor needs to be inverted (1/k) to find the initial function.
• 📌 The key steps for translation involve moving the known equation by the opposite of the given translation vector (A, B).
• 🔄 In reflection scenarios, reflect the known function using the same axis or line as in the problem (e.g., x-axis, y-axis, or y=6).
• ⏳ Rotations around a point O by an angle Alpha require rotating the known function in the reverse direction (e.g., if 90 degrees clockwise, rotate 90 degrees counterclockwise).
• 📐 For dilation, apply the inverse of the scale factor, keeping the center of dilation fixed at O.
• 📂 Reference materials, such as earlier review videos, are available for further explanation of these transformation rules.

Q & A

What are the four types of transformations discussed in the video?

The four types of transformations discussed are translation, reflection, rotation, and dilation.

How do you determine the initial function equation from a translation?

To determine the initial function from a translation, you write the known transformed function first, then apply the inverse of the given translation. For example, if the translation is (A, B), the inverse translation is (-A, -B).

What is the method to determine the initial function equation from a reflection?

To determine the initial function from a reflection, you place the known transformed function first and then apply the same type of reflection as described in the problem. For instance, if the reflection is over the x-axis, you reflect the function over the x-axis.

How do you handle a reflection when the axis is not the x- or y-axis?

If the reflection is over a line such as y = 6, you reflect the function over that specific line, ensuring the reflection matches the axis described in the problem.

What is the procedure for determining the initial function equation from a rotation?

To determine the initial function from a rotation, first write the known transformed function, then apply a rotation by the inverse of the given angle. For example, if the problem states a rotation of 90 degrees, you rotate the function by -90 degrees.

What happens if the rotation angle in the problem is negative?

If the rotation angle is negative, such as -180 degrees, you apply the positive equivalent (180 degrees) to determine the initial function.

How do you determine the initial function equation from a dilation?

To determine the initial function from a dilation, place the known transformed function first, then apply a dilation using the inverse of the given scale factor. If the dilation scale factor is k, you apply 1/k.

What is the relationship between scale factors in dilation when determining the initial function?

The scale factor used to determine the initial function is the reciprocal of the scale factor given in the problem. For example, if the scale factor in the problem is k, you use 1/k for the inverse dilation.

Where can you find more information about the formulas used for these transformations?

More information about the formulas for these transformations can be found in the review videos mentioned in the transcript, including materials on translations, reflections, rotations, and dilations.

Why is it important to memorize the formulas for different transformations?

Memorizing the formulas helps solve transformation problems more quickly and efficiently, as you can easily recall which formula to use for each type of transformation.