Introduction transformations

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Introduction transformations

  1. 1. INTRODUCTION TO TRANSFORMATIONS Objectives: Identify Parent Functions Recognize Types of Transformations
  2. 2. PARENT FUNCTIONS <ul><li>Parent Function - A function that generates a family of functions. </li></ul>
  3. 3. COMMON TYPES OF PARENT FUNCTIONS
  4. 4. More Parent Function Types
  5. 5. Even More Parent Functions
  6. 6. TRANSFORMATIONS <ul><li>Transformations- A change in the position and/or size of a figure or graph. </li></ul>A &quot;transformation” of a parent function preserves the parent function’s structure. <ul><li>There are 3 types of transformations: </li></ul><ul><ul><li>Translation </li></ul></ul><ul><ul><li>Reflection </li></ul></ul><ul><ul><li>Stretch </li></ul></ul>
  7. 7. TRANSLATION <ul><li>Translation- A transformation that moves every point on a figure a given distance in a given direction. </li></ul>&quot;Translation&quot; simply means Shifts … without rotating, stretching or anything else, just shifts.     
  8. 8. REFLECTIONS <ul><li>Reflections- A transformation creating a mirror image of a figure or graph on the opposite side of a line </li></ul>Every point is the same distance from the central (mirror) line ... and ...The reflection has the same size as the original image
  9. 9. Stretch <ul><li>Stretch - a transformation in which the size of a figure or graph changes, but the shape of the figure or graph stays the same. </li></ul>Stretch Stretch in
  10. 10. Transforming Parent Functions <ul><li>Sketch the graph of a f(x) = √x parent function. </li></ul>
  11. 11. Translation of Parent Function <ul><li>Sketch a vertical translation </li></ul> 
  12. 12. <ul><li>Now sketch a horizontal translation. </li></ul> 
  13. 13. Reflection of Parent Function <ul><li>Sketch the parent function of a quadratic. </li></ul>Sketch a vertical refection of the parent function Possible Example: What is the line of reflection?

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