SANGAT JELAS! Rumus TRANSLASI dan DILATASI. TRANSFORMASI FUNGSI. Matematika Kelas 12 [SMA]

Summary

This 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

• 📐 There are four types of function transformations: translation, dilation, reflection, and rotation.
• ➡️ Translation or shifting of a function occurs when the function is moved horizontally or vertically.
• 🧮 For a function y = f(x) translated by AB, the new function is y = f(x - a) + b.
• 🔄 In translation, 'a' represents the horizontal shift. Positive 'a' means shifting to the right, and negative 'a' means shifting to the left.
• ⬆️ 'b' represents the vertical shift. Positive 'b' shifts the function upward, and negative 'b' shifts it downward.
• 📏 Dilation involves resizing the function, either enlarging or reducing it.
• 🔍 When a function y = f(x) undergoes dilation with center O and scale factor k, the new function is y = k * f(x/k).
• 🎯 O is the center of dilation, and 'k' is the scaling factor.
• ✍️ Memorizing these formulas is essential, as they will be used in problem-solving later.
• 📹 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.