[table][br][tr][br][td]Graph transformations[/td][br][td]グラフ変換[/td][br][td]图形变换[/td][br][td]그래프 변환[/td][br][/tr][br][tr][br][td]Translation[/td][br][td]平行移動[/td][br][td]平移[/td][br][td]평행 이동[/td][br][/tr][br][tr][br][td]Reflections[/td][br][td]反転[/td][br][td]镜像[/td][br][td]반사[/td][br][/tr][br][tr][br][td]Vertical stretch[/td][br][td]垂直方向の伸縮[/td][br][td]纵向伸缩[/td][br][td]수직 스트레치[/td][br][/tr][br][tr][br][td]Horizontal stretch[/td][br][td]水平方向の伸縮[/td][br][td]横向伸缩[/td][br][td]수평 스트레치[/td][br][/tr][br][tr][br][td]Composite transformations[/td][br][td]複合変換[/td][br][td]复合变换[/td][br][td]복합 변환[/td][br][/tr][br][tr][br][td]Function[/td][br][td]関数[/td][br][td]函数[/td][br][td]함수[/td][br][/tr][br][tr][br][td]Sin(x)[/td][br][td]サイン(x)[/td][br][td]正弦(x)[/td][br][td]사인(x)[/td][br][/tr][br][/table]

[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]

The graph transformations for the curve of [math]y=sin(x)[/math], works for all functions. When we looked at completing the square and the vertex form [math]y=(x-h)^2+k[/math] we considered the vertex form as a graph transformation the original function, [math]y=x^2[/math]. In function notation this would be [math]y=f(x-h)+k[/math].[br][br]When we investigated the parabola [math]y=ax^2[/math], we looked at it's effect on the concavity. [br][br]Putting it all together can you help clear up this discussion....

These two videos split the ideas into translations (moving) for the first video and the second video stretching/compressing and reflections.

Checking your understanding with exam-style questions[br][br][b]Question 1-4 Practice questions [br][br][/b][b]Exam style - Section A - Short response [/b]Question 5-15, 17, 18, 19, 21, 22, 23,24,25 [br][b]Challenging - Question 16[br][/b][b][br]Exam style - Section B - Long response [/b]Question 26 [br][b]Challenging - Question 27,28[/b]