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Graph Trans (AASL 2.11, AIHL 2.8)

Author:Cliff Packman
Graph transformationsグラフ変換图形变换그래프 변환
Translation平行移動平移평행 이동
Reflections反転镜像반사
Vertical stretch垂直方向の伸縮纵向伸缩수직 스트레치
Horizontal stretch水平方向の伸縮横向伸缩수평 스트레치
Composite transformations複合変換复合变换복합 변환
Function関数函数함수
Sin(x)サイン(x)正弦(x)사인(x)

Inquiry questions

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

Which transformation is represented by the function y = f(x) + b?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

If a graph is reflected over the x-axis, which of the following functions represents this transformation?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

What is the effect of the transformation y = (1/q)f(x) on the graph of y = f(x)?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

If a graph undergoes a horizontal translation of a units to the right, which function would represent this transformation?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Conceptual questions

The graph transformations for the curve of , works for all functions. When we looked at completing the square and the vertex form we considered the vertex form as a graph transformation the original function, . In function notation this would be . When we investigated the parabola , we looked at it's effect on the concavity. Putting it all together can you help clear up this discussion....

William says to get from the red line to the blue line the line is translated up by 1 unit. Julia says to get from the red line to the blue line the line has been translated 1 unit to the left. Who is right? How can we justify this using function notation?

Check my answer

Connor says the blue line has been compressed horizontally to create the red line. Kim says the blue line has been stretched vertically to create the red line. Who is right? How can we justify this using function notation and graph transformations? What are the respective scale factors?

Check my answer

Sen says f(-x) produces a reflection, but in this case what is happening.

Check my answer

Part 2 - Check your understanding

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

Part 3 - Exam-style questions

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

[MAA 2.6] TRANSFORMATIONS

[MAA 2.6] TRANSFORMATIONS.pdf

[MAA 2.6] TRANSFORMATIONS.pdf

[MAA 2.6] TRANSFORMATIONS_solutions

[MAA 2.6] TRANSFORMATIONS_solutions.pdf

[MAA 2.6] TRANSFORMATIONS_solutions.pdf

Lesson Plan- Exploring Graph Transformations in IB DP Mathematics

Lesson Plan- Exploring Graph Transformations in IB DP Mathematics.pdf

Lesson Plan- Exploring Graph Transformations in IB DP Mathematics.pdf

Graph Transformations - Intuition pump (thought experiments and analogies)

Graph Trans.pdf

Graph Trans.pdf

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