Linear Piecewise Function Project Tutorial
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Create a Desmos account using your
school email account
([email protected])
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Follow the link in each lesson to
complete the tasks, writing your
solutions on the answer sheet. Save
your files to your account after each
lesson.
Lesson 1 – Graphing a Line Between Two Points (Task 1: http://bit.ly/2c0LOke )
𝑦 −𝑦
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Find the slope, 𝑚, using 𝑚 = 𝑥2 −𝑥1
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Use point-slope form 𝑦 = 𝑚(𝑥 − 𝑥1 ) + 𝑦1
Write domain restriction with appropriate inequalities.
2
(−3, 4), (4, −1)
𝑦 −𝑦
−1−4
𝑚 = 𝑥2 −𝑥1 = 4−(−3) =
2
1
1
𝑦 = 𝑚(𝑥 − 𝑥1 ) + 𝑦1
−5
7
5
𝑦 = − 7 (𝑥 − (−3)) + 4
5
𝑦 = − 7 (𝑥 + 3) + 4
5
𝑦 = − 7 (𝑥 + 3) + 4{−3 < 𝑥 ≤ 4}
Linear Piecewise Function Project Tutorial
Lesson 2 – Jumps and Gaps (Task 2: http://bit.ly/2ca1KqO )
Jumps
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Endpoints will share x-values and will have different y-values.
Make sure endpoints do not violate functionality (pass the vertical line test).
Example: http://bit.ly/2c2t1u0
Gaps
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Endpoints will share y-values and will have different x-values.
Example: http://bit.ly/2ciyFWS
Jumps and Gaps
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Example: http://bit.ly/2cfQl3p
Lesson 3 – Holes (Task 3: https://www.desmos.com/calculator/bgbaijojms )
Lines must meet at the same not-included point to create a hole. The simplest way to achieve this is to
use the same point, (𝒙𝟏 , 𝒚𝟏 ), when writing both equations in point-slope form.
*Note – lines that meet at an included point are considered continuous throughout the interval, not a
hole.
Lesson 4 – Vertical Shifts (Task 4: http://bit.ly/2c34RdF )
To animate a line moving up and down, you need to add a slider parameter to your equation.
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When using point slope form, add or subtract a parameter to right side of 𝒚𝟏
𝒚 = 𝒎(𝒙 − 𝒙𝟏 ) + 𝒚𝟏 + 𝒅 {𝒍𝒆𝒇𝒕 < 𝒙 < 𝒓𝒊𝒈𝒉𝒕}
Example: http://bit.ly/2cuV70m
Linear Piecewise Function Project Tutorial
Lesson 5 – Horizontal Shifts (Task 5: http://bit.ly/2cPJzm2 )
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When using point slope form, subtract a parameter to right side of 𝒙𝟏 .
You must also add that same parameter on both the left and right restrictions.
𝒚 = 𝒎(𝒙 − 𝒙𝟏 − 𝒄) + 𝒚𝟏 {𝒍𝒆𝒇𝒕 + 𝒄 < 𝒙 < 𝒓𝒊𝒈𝒉𝒕 + 𝒄}
*Note – for horizontal lines, only add parameters to the restriction.
http://bit.ly/2cmLcWO
Lesson 6 – Moving Points (Task 6: http://bit.ly/2ci3Dwi )
Lesson 6 Example - http://bit.ly/2cjQCUM
Solo Moving Point
1. To create moving points, you must first
define a function for it to move along, using
function notation (𝑓(𝑥) =, 𝒌(𝒙) =, 𝑒𝑡𝑐. ).
2. Next, define a coordinate (𝒙, 𝒇(𝒙)), using a
parameter and the function you defined
(𝒃, (𝒌(𝒃)).
3. Finally, add the slider, and make sure to adjust the slider’s restriction to match your function. Turn off
your equation and your point will move on its own.
Linear Piecewise Function Project Tutorial
Moving Endpoints
1. To create endpoints that move along with your moving platforms and ramps, you must define your
equation using function notation, creating a second line on top of your platform/ramp.
2. Create two coordinates using your function,
with your endpoints as the x-values.
3. Turn off your second line, change the color
and style of your endpoints to match your
function and its restrictions.
*Note, to make moving endpoints on horizontally moving platforms, you must include the same
parameter you use to make your platform move as the x-value for your endpoints (see example 3).
Linear Piecewise Function Project Tutorial
Lesson 7 - Other Functions and Miscellaneous Ideas (Task 7: http://bit.ly/2cGeeBJ )
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Moving Liquid - http://bit.ly/2co9Qty
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Staircases - http://bit.ly/2cc8Vyw
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Cirlces - http://bit.ly/2ch5P74
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Floating Blocks - http://bit.ly/2cimSXH
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Triangles - http://bit.ly/2cce8GC
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Smashers - http://bit.ly/2c2k8f7
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Bridges - http://bit.ly/2chcsq8