AP Calculus

# AP Calculus Summer Packet Topic 5 Video

Created 2 years ago

Duration 0:19:26
65
Transformations
Slide Content
Tags: AP Calculus
1. ### Slide 1 - AP Calculus Summer Packet

• Topic 5: Transformations
2. ### 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. ### Slide 3 - Transformations on

• Slide up 3 units from f(x)
• Slide left 2 units from f(x)
4. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### Slide 13 - Contact

• ddestefa@k12.wv.us