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Understanding Transformations: Reflection, Translation, and Scaling Step-by-Step

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In this tutorial, we analyze the effects of various transformations on a curve. Initially, the curve undergoes three transformations: reflection about the y-axis, translation 4 units in the positive x-direction, and scaling parallel to the y-axis by a factor of 2. To determine the original curve, we reverse these transformations - undoing the reflection, translating 4 units in the negative x-direction, and scaling parallel to the y-axis by a factor of ½. This step-by-step guide clarifies the process of unraveling transformations in mathematical functions.

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Understanding Transformations: Reflection, Translation, and Scaling Step-by-Step

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Presentation Transcript

  1. Tutorial 4 Question 5 • First, let’s write out what happened originally. A: Reflection about the y-axis; B: Translation of 4 units in the positivex-direction; C: Scaling parallel to the y-axis by a factor of 2.

  2. Tutorial 4 Question 5 • Since we have the final transformed curve and we’re interested in the original curve, we undo the transformations in reverse order to figure it out. Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  3. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ . Equation effect: replace with

  4. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ . Equation effect: replace with

  5. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  6. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  7. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Equation effect: replace with (use brackets to be safe) Undo C: Scaling parallel to the y-axis by a factor of ½ .

  8. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Equation effect: replace with (use brackets to be safe) Undo C: Scaling parallel to the y-axis by a factor of ½ .

  9. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  10. Tutorial 4 Question 5 Undo A: Reflection about the y-axis;Equation effect: replace with (use brackets to be safe) Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  11. Tutorial 4 Question 5 Undo A: Reflection about the y-axis;Equation effect: replace with (use brackets to be safe) Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  12. Tutorial 4 Question 5 Undo A: Reflection about the y-axis; Undo B: Translation of 4 units in the negativex-direction; Undo C: Scaling parallel to the y-axis by a factor of ½ .

  13. Tutorial 4 Question 5 The original curve is

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