SANGAT JELAS! Rumus TRANSLASI dan DILATASI. TRANSFORMASI FUNGSI. Matematika Kelas 12 [SMA]
Summary
TLDRThis video explains four types of function transformations: translation, dilation, reflection, and rotation. The focus is on translation, where a function y = f(x) is shifted horizontally by 'a' and vertically by 'b', resulting in y = f(x - a) + b. A positive 'a' shifts right, while a negative 'a' shifts left; a positive 'b' shifts up, and a negative 'b' shifts down. The video also introduces dilation, which enlarges or shrinks a function. If y = f(x) is dilated with center O and scale factor k, the transformed function becomes y = k * f(x/k).
Takeaways
- ๐ There are four types of function transformations: translation, dilation, reflection, and rotation.
- โก๏ธ Translation or shifting of a function occurs when the function is moved horizontally or vertically.
- ๐งฎ For a function y = f(x) translated by AB, the new function is y = f(x - a) + b.
- ๐ In translation, 'a' represents the horizontal shift. Positive 'a' means shifting to the right, and negative 'a' means shifting to the left.
- โฌ๏ธ 'b' represents the vertical shift. Positive 'b' shifts the function upward, and negative 'b' shifts it downward.
- ๐ Dilation involves resizing the function, either enlarging or reducing it.
- ๐ When a function y = f(x) undergoes dilation with center O and scale factor k, the new function is y = k * f(x/k).
- ๐ฏ O is the center of dilation, and 'k' is the scaling factor.
- โ๏ธ Memorizing these formulas is essential, as they will be used in problem-solving later.
- ๐น Additional videos will cover more applications and problem-solving involving these transformations.
Q & A
What are the four types of function transformations mentioned in the transcript?
-The four types of function transformations mentioned are translation, dilation, reflection, and rotation.
What is the meaning of 'translation' in the context of function transformation?
-Translation refers to shifting a function horizontally or vertically. It can be represented as y = f(x - a) + b, where 'a' is the horizontal shift and 'b' is the vertical shift.
How does the value of 'a' affect the function in a translation?
-The value of 'a' determines the horizontal shift: if 'a' is positive, the function shifts to the right; if 'a' is negative, the function shifts to the left.
How does the value of 'b' affect the function in a translation?
-The value of 'b' determines the vertical shift: if 'b' is positive, the function shifts upward; if 'b' is negative, the function shifts downward.
What does dilation refer to in function transformation?
-Dilation refers to enlarging or shrinking a function. It involves scaling the function based on a factor 'k' from a center point, often the origin (O).
What happens to a function when it is dilated with a scale factor of k?
-When a function y = f(x) is dilated with a scale factor of k, the transformed function becomes y = k * f(x/k).
What is the center point of dilation in the context provided?
-The center point of dilation in the provided context is the origin, denoted as point O.
What is the significance of the factor 'k' in dilation?
-The factor 'k' determines the scale of dilation: if k > 1, the function is enlarged; if 0 < k < 1, the function is shrunk.
How do you apply the dilation formula to a function?
-To apply dilation, you take the original function y = f(x) and transform it using the formula y = k * f(x/k), where 'k' is the scale factor.
What is the expected follow-up to this video lesson on transformations?
-The follow-up will include exercises and applications of these formulas in future videos.
Outlines
๐ข Introduction to Function Transformations
This paragraph introduces the concept of function transformations, outlining four main types: translation, dilation, reflection, and rotation. The focus of this discussion is on translation, explaining how a function y = f(x) can be shifted horizontally and vertically. The horizontal shift (a) moves the graph left or right, with positive a indicating a right shift and negative a indicating a left shift. The vertical shift (b) moves the graph up or down, where a positive b means an upward shift and a negative b means a downward shift.
๐ Dilation in Function Transformations
This paragraph dives into the concept of dilation, which either enlarges or shrinks the graph of a function. When a function y = f(x) undergoes dilation, there is a central point of dilation (denoted as O) and a scaling factor (denoted as k). The formula for this transformation becomes y = k * f(x/k), where k determines the degree of scaling. A detailed explanation is provided to help understand how this transformation works, with an emphasis on remembering the formula for future problem-solving.
Mindmap
Keywords
๐กTransformasi Fungsi
๐กTranslasi
๐กDilatasi
๐กRefleksi
๐กRotasi
๐กy = f(x)
๐กPergeseran
๐กPusat O
๐กFaktor Skala
๐กy = k * f(x/k)
Highlights
There are four types of function transformations: translation, dilation, reflection, and rotation.
Translation refers to the shifting of a function either horizontally or vertically.
If a function y = f(x) is translated by a vector (a, b), the resulting function is y = f(x - a) + b.
In a translation, 'a' represents the horizontal shift: positive 'a' moves the function to the right, negative 'a' moves it to the left.
'b' represents the vertical shift: positive 'b' moves the function upward, while negative 'b' shifts it downward.
Dilation involves enlarging or shrinking the function with respect to a central point, typically the origin.
If a function y = f(x) is dilated with center O (origin) and scale factor k, the transformed function becomes y = k * f(x/k).
Dilation can either increase or decrease the size of the function, depending on the value of k.
A positive k value greater than 1 enlarges the function, while a value between 0 and 1 shrinks it.
Reflection and rotation are the other two types of transformations but are not discussed in detail here.
Translations shift the graph horizontally or vertically without changing its shape.
Dilation affects the scale of the graph, either expanding or contracting it based on the scale factor k.
Understanding how a function transforms under these operations is crucial for analyzing changes in its behavior.
The formulas for translation and dilation are important to memorize for solving transformation problems.
Examples and application problems involving these transformations will be discussed in future videos.
Transcripts
Hai saya akan menjelaskan tentang
transformasi fungsi transformasi fungsi
itu ada empat macam translasi
dilatasi
refleksi dan
rotasi sekarang yang kita bahas adalah
tentang translasi atau
pergeseran kalau ada fungsi y = FX akan
ditranslasi
sebesar
AB maka bayangannya adalah fungsi y = FX
- a + b di mana Kalau translasinya itu
Ab itu artinya A itu adalah nilai
pergeseran ke kanan atau ke kiri kalau
digeser ke kanan maka nilai a-nya itu
plus kalau digesernya ke kiri maka nilai
a-nya itu Min sedangkan b adalah
pergeseran ke atas atau ke bawah kalau
gesernya ke atas maka nilai b-nya itu
plus kalau gesernya ke bawah nilai b-nya
itu Min gitu ya lalu berikutnya ada
dilatasi dilatasi itu memperbesar atau
memperkecil diperbesar atau diperkecil
kalau ada fungsi y =
FX didilatasi dengan pusat O jadi titik
O ini adalah pusat dilatasi dan K adalah
faktor skala
perbesaran Saya ulang kalau ada fungsi y
= FX didilatasi dengan pusat
O dan faktor skala perbesaran k maka
bayangannya adalah fungsi y
= k * f x/k
oke Ini harus kalian hafal dan nanti
soal-soal penerapannya rumus-rumus ini
akan ada di video-video selanjutnya oke
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