AP Calculus Summer Packet Topic 5 Video

Transformations

AP Calculus
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AP Calculus Summer Packet Topic 5 Video

Created 2 years ago

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Transformations
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Tags: AP Calculus
  1. AP Calculus Summer Packet

    Slide 1 - AP Calculus Summer Packet

    • Topic 5: Transformations
  2. Translations/Slides

    Slide 2 - Translations/Slides

    • Any transformation that causes the function to move vertically and/or horizontally
    • The shape of the function is unchanged (not stretched/nor shrunk)
    • is a transformation that moves the function up/down a units
    • is a transformation that moves the function left/right a units
    • Use the example for the next several slides
  3. Transformations on

    Slide 3 - Transformations on

    • Slide up 3 units from f(x)
    • Slide left 2 units from f(x)
  4. Reflections

    Slide 5 - Reflections

    • Any transformation that reflects a function over a line, typically the x or y-axes
    • The shape of the function is unchanged.
    • is a reflection over the y-axis
    • is a reflection over the x-axis
  5. Stretch/Shrinks by n

    Slide 6 - Stretch/Shrinks by n

    • is a vertical stretch by n if
    • Same as a horizontal shrink by
    • is a vertical shrink by n if
    • Same as a horizontal stretch by
    • These transformations do not preserve the shape of the function
  6. Combination Transformations on

    Slide 7 - Combination Transformations on

    • Horizontal shift right 4 units and a reflection over the x-axis on f(x)
    • Vertical stretch by 3 and a vertical shift up 5
  7. Unconventional Transformations on

    Slide 9 - Unconventional Transformations on

    • These don’t necessarily follow an exact pattern for all function and take a little more analysis.
    • Most would think this is a vertical stretch by 3
    • Most would say a vert. stretch by 27, but
    • Final transformation would be a vertical stretch by 27 and vertical shift down 26
  8. Unconventional Transformations on

    Slide 10 - Unconventional Transformations on

    • These don’t necessarily follow an exact pattern for all function and take a little more analysis.
    • need to treat as a piecewise, find the functions/domains
  9. Unconventional Transformations on

    Slide 11 - Unconventional Transformations on

    • Absolute value will not change if f(x) is positive
    • , so the only transformation will occur is a reflection over the x-axis where x<-1
  10. Contact

    Slide 13 - Contact

    • ddestefa@k12.wv.us