describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b)...
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![Page 1: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/1.jpg)
Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2b) p(x)=f(x+2)c) h(x)=-f(x)
Do Now
![Page 2: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/2.jpg)
Unit 1 Test
• Logs – be specific! What do you need to practice more on?
• Your proof of practice can be correcting old quick checks and the recent Unit 1 test.
• Schedule a time with me if you want a retake.
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Describe or draw the graph of g(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2b) p(x)=f(x+2)
Do Now
![Page 4: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/4.jpg)
I. Domain/Input and Range/Output Relationships
LT: 2A I can identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(kx), and f(x +k) for specific values of k
(both positive and negative), including using technology. I can find the value of k given the graphs. I can recognize even
(symmetric about the y-axis) and odd (symmetric about the origin) functions from their graphs and algebraic expressions)
Notes Title: Function Transformations Pt. 1
![Page 5: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/5.jpg)
Vocabulary
A Vertical shift is a translation with out rotation or distortion in the up –down direction.
A Horizontal shift is a translation with out rotation or distortion in the left -right direction.
Slide
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Visual
F(x) Vertical ShiftF(x)+ k
Horizontal ShiftF(x + k)
(0,0) (0,k) (-k,0)
Parent
Function
Adding to the Range/
output
Adding to the Domain/input
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Vertical Shifts: UP? DOWN?
UP for k > 0DOWN for k < 0
(0,k)
(0,-k)
Positive Number
Negative Number
Vertical ShiftF(x)-k
Vertical ShiftF(x)+ k
![Page 8: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/8.jpg)
Horizontal ShiftF(x - k)
Horizontal shifts: LEFT? RIGHT?
RIGHT for k < 0LEFT for k > 0
(-k,0)
(k,0)
Positive NumberNegative
Number
Horizontal ShiftF(x + k)
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Example 1Given that f(x)=x2, Describe the Vertical and Horizontal Shifts of g(x) =(x+1)2 - 4
Vertical Shift
Horizontal Shift
The graph of f(x) completes a vertical shift of 4 down and a horizontal shift of 1 to the left
x+1 = 0 x = -1
Use Geogebra as a visual
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Example 2 The trajectory of the canon ball is shown below. Where should the canon be rolled to
in order to hit the target?
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Cheat SheetQuadratic
2)( xxf Linear Absolute Value
bmxxf )( xxf )(
Square Rootxxf )( Cubic
3)( xxf
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ConnectionsInput(Domain) / Output(Range)
Function
Transformation (Translation)
Horizontal Shift f(x+k)
Vertical Shift f(x) +k
Parent Function
Quadratic
Linear
Exponential
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Do Now
What do you think the original parent function’s equation looked like?
![Page 14: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/14.jpg)
Vertical Shifts: UP? DOWN?
UP for k > 0DOWN for k < 0
(0,k)
(0,-k)
Positive Number
Negative Number
Vertical ShiftF(x)-k
Vertical ShiftF(x)+ k
![Page 15: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/15.jpg)
Horizontal ShiftF(x - k)
Horizontal shifts: LEFT? RIGHT?
RIGHT for k < 0LEFT for k > 0
(-k,0)
(k,0)
Positive NumberNegative
Number
Horizontal ShiftF(x + k)
![Page 16: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/16.jpg)
Example 3
Name the shifts necessary to go from
to
1)3( 2 xy
4)7( 2 xy
-10 +5
Horizontal shift to
the right
Vertical shift, up
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Today…
1. Translations on Parent Functions– Use your notes!
2. Goal Problem
![Page 18: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/18.jpg)
Goal Problems (LT 2A #1)
Recall & ReproductionsIdentify the parent graph and the shifts from f(x) to g(x) :
RoutineName the shifts
necessary to go from
to
![Page 19: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/19.jpg)
Assessment
• If you got both correct, do “Jelly”• If you got the first (graph) problem correct but
not the second one, do “Peanut”• If you got none of them correct, do “Butter”
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Do Now
![Page 21: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/21.jpg)
Active Sense-Making Recall & Reproductions
Matching Graphs and shifts
cards
Routine
Gallery Walk on the walls
Still need this.
Non-Routine
![Page 22: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/22.jpg)
A.) Vertical & Horizontal Scale factor.
I.) Domain/Input & Range/Output Relationship
The growth of a Function is increased when the domain or range is multiplied scale factor of k.
f(kx) kf(x)
Increasing the Domain by a multiple of k
Increasing the Range by a
multiple of k
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B.) Visual
I.) Domain/Input & Range/Output Relationship
Compare the rate of change
for each function
IncreasesFaster
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C.) Process (ex)
I.) Domain/Input & Range/Output Relationship
![Page 25: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/25.jpg)
D. Connections
Input(Domain) / Output(Range)
Function
Transformation (Translation)
Horizontal Shift f(x+k)
Vertical Shift f(x) +k
Transformation (Stretching)
Parent Function
Quadratic
Linear
Exponential
![Page 26: Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now](https://reader035.vdocuments.mx/reader035/viewer/2022062516/56649dde5503460f94ad7c75/html5/thumbnails/26.jpg)
Goal Problems (LT 2A #1)
Recall & Reproductions
Compare between f(x) and g(x):
1.) f(x) = 4x2 ; g(x)= 2x2
2.) f(x)= (4x)2; g(x)=(2x)2
Routine
Compare function’s growth rate is increasing
faster:f(x) = 3x2
Org(x)=(3x)2