[table][br][tr][br][td]English[/td][br][td]Japanese[/td][br][td]Korean[/td][br][td]Chinese Simplified[/td][br][/tr][br][tr][br][td]Graph Transformation[/td][br][td]グラフ変換[/td][br][td]그래프 변환[/td][br][td]图形变换[/td][br][/tr][br][tr][br][td]Translation[/td][br][td]平行移動[/td][br][td]이동[/td][br][td]平移[/td][br][/tr][br][tr][br][td]Reflection[/td][br][td]反射[/td][br][td]반사[/td][br][td]反射[/td][br][/tr][br][tr][br][td]Dilation/Stretch[/td][br][td]拡大/伸長[/td][br][td]확대/늘리기[/td][br][td]膨胀/伸展[/td][br][/tr][br][tr][br][td]Compression[/td][br][td]圧縮[/td][br][td]압축[/td][br][td]压缩[/td][br][/tr][br][tr][br][td]Absolute Value Transformation[/td][br][td]絶対値変換[/td][br][td]절대값 변환[/td][br][td]绝对值变换[/td][br][/tr][br][tr][br][td]Phase Shift[/td][br][td]位相シフト[/td][br][td]위상 이동[/td][br][td]相位移动[/td][br][/tr][br][tr][br][td]Squaring Function[/td][br][td]二乗関数[/td][br][td]제곱 함수[/td][br][td]平方函数[/td][br][/tr][br][tr][br][td]Amplitude[/td][br][td]振幅[/td][br][td]진폭[/td][br][td]振幅[/td][br][/tr][br][tr][br][td]Period[/td][br][td]周期[/td][br][td]주기[/td][br][td]周期[/td][br][/tr][br][tr][br][td]Axis Crossing Points[/td][br][td]軸交差点[/td][br][td]축 교차점[/td][br][td]轴交点[/td][br][/tr][br][tr][br][td]Reciprocal Function[/td][br][td]逆関数[/td][br][td]역함수[/td][br][td]倒数函数[/td][br][/tr][br][/table][br]

[table][br][tr][br] [td][b]Factual Inquiry Questions[/b][br] [list][br] [*]What is a graph transformation, and what are the main types of transformations?[br] [*]How does each type of transformation (translation, reflection, dilation/stretch, and compression) affect the graph of a function?[br] [/list][br] [/td][br] [td][b]Conceptual Inquiry Questions[/b][br] [list][br] [*]Why is it important to understand the effect of transformations on the parent function when studying graph transformations?[br] [*]How do transformations help in understanding the behavior and properties of more complex functions based on their graphical representations?[br] [/list][br] [/td][br] [td][b]Debatable Inquiry Questions[/b][br] [list][br] [*]How significant are graph transformations in fields that rely heavily on visual data representation, such as engineering and computer science?[br] [*]With the advancement of graphing calculators and software, is the manual skill of applying graph transformations becoming obsolete, or does it still hold value?[br] [/list][br] [/td][br][/tr][br][/table][br]

Exploration Title: Waves of Transformation[br][br]Objective:[br]Your task is to become a Function Transformer, using the power of mathematical operations to alter the shape and position of the classic sine wave.[br][br]Mission Steps:[br][br]1. The Original Wave:[br] - Start with the original function sin(x). Observe its amplitude, period, and axis crossing points. [br] - Discuss the real-life scenarios where the sine wave is observed (e.g., sound waves, alternating current).[br][br]2. Absolute Changes:[br] - Apply the absolute value transformation, |f(x)|, and observe how the sine wave changes. [br] - What happens to the negative values of the sine wave, and how does this affect its graph?[br][br]3. Flipping and Shifting:[br] - Now, explore the effects of adding a constant to the function, f(x + b). How does this affect the wave's phase?[br] - Also, explore the reflection of the wave over the x-axis by looking at -f(x). How does the wave invert?[br][br]4. Squaring the Wave:[br] - Take the function to a new dimension by squaring it, [f(x)]^2. [br] - How does squaring the function affect the period and amplitude of the wave?[br][br]Questions for Investigation:[br][br]1. Inquiry Challenge:[br] - Can you predict the graph of the function before applying the transformation?[br][br]2. Real-World Connection:[br] - How would these transformations represent real-world phenomena, such as sound waves traveling through different media?[br][br]3. Mathematical Detective:[br] - Given a transformed wave, can you deduce the series of transformations that led to it?[br][br]4. Creative Twist:[br] - Use the transformations to create a unique wave pattern and describe its properties.[br][br]Engagement Activities:[br][br]- "Wave Maker" Contest: Who can create the most unique wave using the applet's transformations?[br]- "Guess the Transformation" Game: Show a transformed wave and let participants guess the transformation applied.[br][br]Throughout the investigation, the Function Transformers will learn the power of mathematical operations and their visual outcomes on graphs, all while having fun with waves.[br]