Graph trans. (AAHL 2.16)
Keywords
| English | Japanese | Korean | Chinese Simplified |
| Graph Transformation | グラフ変換 | 그래프 변환 | 图形变换 |
| Translation | 平行移動 | 이동 | 平移 |
| Reflection | 反射 | 반사 | 反射 |
| Dilation/Stretch | 拡大/伸長 | 확대/늘리기 | 膨胀/伸展 |
| Compression | 圧縮 | 압축 | 压缩 |
| Absolute Value Transformation | 絶対値変換 | 절대값 변환 | 绝对值变换 |
| Phase Shift | 位相シフト | 위상 이동 | 相位移动 |
| Squaring Function | 二乗関数 | 제곱 함수 | 平方函数 |
| Amplitude | 振幅 | 진폭 | 振幅 |
| Period | 周期 | 주기 | 周期 |
| Axis Crossing Points | 軸交差点 | 축 교차점 | 轴交点 |
| Reciprocal Function | 逆関数 | 역함수 | 倒数函数 |
Inquiry questions
Factual Inquiry Questions
| Conceptual Inquiry Questions
| Debatable Inquiry Questions
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Waves of Transformation
Exploration Title: Waves of Transformation
Objective:
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.
Mission Steps:
1. The Original Wave:
- Start with the original function sin(x). Observe its amplitude, period, and axis crossing points.
- Discuss the real-life scenarios where the sine wave is observed (e.g., sound waves, alternating current).
2. Absolute Changes:
- Apply the absolute value transformation, |f(x)|, and observe how the sine wave changes.
- What happens to the negative values of the sine wave, and how does this affect its graph?
3. Flipping and Shifting:
- Now, explore the effects of adding a constant to the function, f(x + b). How does this affect the wave's phase?
- Also, explore the reflection of the wave over the x-axis by looking at -f(x). How does the wave invert?
4. Squaring the Wave:
- Take the function to a new dimension by squaring it, [f(x)]^2.
- How does squaring the function affect the period and amplitude of the wave?
Questions for Investigation:
1. Inquiry Challenge:
- Can you predict the graph of the function before applying the transformation?
2. Real-World Connection:
- How would these transformations represent real-world phenomena, such as sound waves traveling through different media?
3. Mathematical Detective:
- Given a transformed wave, can you deduce the series of transformations that led to it?
4. Creative Twist:
- Use the transformations to create a unique wave pattern and describe its properties.
Engagement Activities:
- "Wave Maker" Contest: Who can create the most unique wave using the applet's transformations?
- "Guess the Transformation" Game: Show a transformed wave and let participants guess the transformation applied.
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.
What is the transformation applied to the original function sin(x) to obtain the graph of y=sin|x| ?
The transformation 1/f(x) applied to y = sin(x) would result in which of the following?
If the original function y = sin(x) is squared, i.e., y = sin(x))^2 , which of the following features will the new graph exhibit?
