MUDAH! Cara Menentukan Persamaan Awal Fungsi pada Transformasi TRANSFORMASI FUNGSI. Matematika Kl 12
Summary
TLDRThis 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.
Outlines
🧑🏫 Introduction to Determining the Original Equation of a Function
This section introduces the topic of determining the original function's equation through transformation methods, such as translation, reflection, rotation, and dilation. The speaker explains that solving these problems involves reversing the transformation provided in the question to find the original function equation. The explanation begins with translation, where the solution involves applying the inverse of the given translation (denoted as AB) to the image of the function. If the transformation involves A and B, the solution requires using -A and -B to obtain the original function. This method is reinforced by referencing previous video lessons that cover translation functions.
📏 Solving for the Original Equation via Reflection, Rotation, and Dilation
The second part discusses how to find the original function through reflection, rotation, and dilation. For reflection, the process involves applying the same reflection provided in the problem to the image function, such as reflecting across the x-axis or any given line. For rotation, the function image is rotated in the opposite direction from what is specified in the problem (for example, if the function was rotated by 90°, the original function is obtained by rotating it -90°). For dilation, the function image is scaled using the reciprocal of the given scaling factor. Each of these methods uses specific formulas, which are found in previously mentioned video reviews. The speaker concludes by encouraging viewers to refer back to earlier lessons on transformation functions for deeper understanding.
Mindmap
Keywords
💡Transformation
💡Translation
💡Reflection
💡Rotation
💡Dilation
💡Inverse Transformation
💡Center of Rotation
💡Scale Factor
💡Equation of Image
💡Original Equation
Highlights
Introduction to the concept of transformations: translation, reflection, rotation, and dilation.
In some problems, the initial function equation is asked instead of the transformed equation.
To determine the initial function by translation, the equation is translated using the opposite of the translation in the problem.
For example, if the translation is AB, the opposite translation would be -A, -B.
The key idea is to use the opposite transformation when reversing the process to find the initial equation.
For reflection, the initial function is found by applying the same type of reflection as given in the problem.
If the reflection is over the x-axis or y = constant, the same reflection is applied to reverse the transformation.
When determining the initial function through rotation, the opposite angle of rotation is used.
If the rotation angle in the problem is 90 degrees, the reverse process would use -90 degrees.
For dilation, the inverse of the scaling factor is used to reverse the transformation.
If the dilation factor is k, the reverse process would use a scaling factor of 1/k.
Understanding the reverse process for each type of transformation is crucial for solving problems related to the initial function.
The importance of remembering and using transformation formulas is emphasized for quick problem-solving.
Each transformation type (translation, reflection, rotation, dilation) has its own set of rules for reversing the process to find the initial function.
The video provides examples and further explanations for determining the initial function from the given transformations.
Transcripts
[Musik]
Halo dengan
teacher kali ini saya akan membahas cara
menentukan persamaan awal fungsi oleh
suatu
transformasi kalian sudah belajar
transformasi itu ada empat macam
translasi refleksi dan dilatasi nah
dalam soal-soal transformasi itu tidak
selalu persamaan bayangan yang
ditanyakan kadang-kadang yang ditanyakan
persamaan
awalnya Nah untuk menyelesaikan itu
caranya berbeda untuk translasi refleksi
rotasi dan
dilatasi kita akan pelajari
perhatikan yang pertama menentukan
persamaan awal fungsi oleh translasi ab
jadi dalam soal diketahui translasinya
AB lalu diketahui juga persamaan
bayangan
fungsi ditanyakan persamaan awalnya yang
mana itu caranya persamaan bayangan
fungsi yang diketahui itu ditulis di
depan kemudian kita translasikan tetapi
dengan lawan dari translasi dalam soal
kalau soalnya translasinya AB maka
untuk mencari persamaan awal itu kita
Trans persamaan bayangan kita
translasikan dengan lawan dari translasi
dalam soal kalau mulanya a maka ini
menjadi a lalu B menjadi -b Nah nanti
jawabannya itu adalah persamaan awal
fungsi yang
ditanyakan jelas ya lah ini
mengerjakannya Bagaimana mengerjakannya
ya kita kerjakan memakai rumus
ASI yang sudah ada di video review
materi yang
pertama kalian bisa lihat ulang kalau
lupa itu persama cara
menentukan persamaan bayangan
translasi gitu ya tetapi ini sekarang
yang di depan ini bukan persamaan awal
tetapi persamaan bayangannya itu kita
taruh di depan kita translasikan dengan
lawan dari translasi soal itu nanti
jawabannya adalah persamaan awal fungsi
yang
ditanyakan lalu nomor dua menentukan
persamaan awal fungsi oleh suatu
refleksi jika diketahui persamaan
bayangan
fungsi nah caranya mirip kalau
ditanyakan persamaan awal maka persamaan
bayangan fungsi yang diketahui itu kita
taruh di
depan lalu kita refleksikan dengan
refleksi dalam soalnya itu jadi refleksi
ini sama kalau refleksinya terhadap apa
sumbu x maka ini juga refleksi terhadap
sumbu x kalau ini refleksi terhadap
garis y = 6 maka ini juga refleksinya
terhadap garis y = 6 jadi sama persis ya
cuma persamaan bayangan fungsinya kita
letakkan di depan kemudian kita
refleksikan sesuai dengan refleksi dalam
soal maka bayangan yang diperoleh ini
adalah persamaan awal fungsi yang
ditanyakan nah rumusnya refleksi ini
bagaimana itu bisa kalian lihat di video
review materi yang kedua yang materi
transformasi lalu yang ketiga menentukan
persamaan awal fungsi oleh
rotasi O
Alfa jika diketahui persamaan fungsi ini
O itu titik pusat rotasinya Alfa itu
sudut
perputarannya maka caranya untuk
menentukan persamaan awal itu persamaan
bayangan dalam soal kita letakkan di
depan kemudian kita
rotasikan dengan pusat O tapi sudut
putarnya lawan dari soal yang diketahui
kalau soalnya perputarannya Alfa
maka kita kerjakan dengan perputaran
Alfa begitu ya kalau alf-anya 90 derajat
dalam soal maka untuk mengerjakan
mencari persamaan
awal persamaan bayangan itu kita
rotasikan dengan pusat O tapi ini tadi
kan 90 ini -90
derajat kalau Soalnya ini Min 180
derajat maka di sini lawannya 180
derajat
maka jawabannya adalah persamaan awal
fungsi yang ditanyakan nah rumus-rumus
tentang rotasi itu ada di review
materi
ketiga pada materi transformasi ya bisa
kalian lihat ulang kalau kalian lupa
lalu yang keempat menentukan persamaan
awal fungsi oleh dilatasi o k jika
diketahui persamaan bayangannya ini
dilatas ya pusatnya o k itu faktor skala
perbesaran nah caranya persamaan
bayangan fungsi yang diketahui dalam
soal kita tulis di depan kemudian kita
dilatasikan dengan pusat O tetapi faktor
skalanya ini 1/k berarti kebalikannya
faktor skala dalam soal soalnya
k kita kerjakan dengan faktor skala 1/k
maka jawabannya nanti adalah persamaan
awal fungsi yang
ditanyakan eh rumus-rumus dilatasi itu
ada di review materi di video review
materi yang
pertama sama dengan translasi ya
translasi juga di video review materi
yang pertama translasi dan dilatasi
kalau kalian lupa kalian lihat lagi
rumus-rumusnya kalian perlu ya
menghafalkan rumus-rumus supaya Kalau
mengerjakan soal bisa cepat ingat rumus
mana yang akan
dipakai
eh tentang ini soal nomor 1 tentang
menentukan persamaan awal fungsi oleh
translasi itu sudah ada di video soal
nomor 12 Jadi kalian bisa langsung
melihat video soal nomor 12 contoh soal
menentukan persamaan awal fungsi oleh
translasi
Oke sukses
5.0 / 5 (0 votes)