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1.3Transforming Linear Functions.notebook
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1.3Transforming Linear Functions
Linear Parent Function
f(x)=x
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Horizontal Shifts
Parent Function: f(x)=x
Horizontal Shift Left: f(x)=(x+a)
f(x)=(xa)
Parent Function: f(x)=x
Horizontal Shift Right:
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Examples
1. Horizontal Shift Left 3
Parent Function: f(x)=x
New Function: f(x)=(x+3)
2. Horizontal Shift Right 5
Parent Function: f(x)=x
New Function: f(x)=(x5)
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You try!
1. Horizontal Shift Left 10
Parent Function:
New Function:
2. Horizontal Shift Right 6
Parent Function:
New Function:
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Vertical Shifts
Parent Function: f(x)=x
Vertical Shift Up: f(x)=x+a
Parent Function: f(x)=x
Vertical Shift Down: f(x)=xa
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Examples
1. Vertical Shift Up 3
Parent Function: f(x)=x
New Function: f(x)=x+3
2. Vertical Shift Down 5
Parent Function: f(x)=x
New Function: f(x)=x5
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You try!
1. Vertical Shift Up 7
Parent Function:
New Function:
2. Vertical Shift Down 10
Parent Function:
New Function:
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Combining Horizontal and Vertical Shifts1. Horizontal Shift Left 6 and Vertical Shift Down 2
Parent Function: f(x)=x
New Function: f(x)=(x+6)2
2. Horizontal Shift Right 3 and Vertical Shift Up 7
Parent Function: f(x)=x
New Function: f(x)=(x3)+7
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You try!1. Horizontal Shift Left 8 and Vertical Shift Down 4
Parent Function:
New Function:
2. Horizontal Shift Right 13 and Vertical Shift Up 15
Parent Function:
New Function:
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Create five of your own transformations based off the linear parent function. You should create the following:
1. One Horizontal Shift Left
2. One Horizontal Shift Right
3. One Vertical Shift Up
4. One Vertical Shift Down
5. One Combining a Horizontal and Vertical Shift
You should label the parent function, the new function, and how many units you are moving in each direction for each problem.
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September 3, 2013
Graph the following functions and their parent function.
1. f(x)=x+4
2. f(x)=(x3)+2
3. f(x)=(x1)
4. f(x)=x5
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Translating and Reflecting Linear FunctionsLet g(x) be the indicated transformation of f(x). Write the rule for g(x).
A. f(x)=2x+3; vertical translation 4 units up
New Function:
1.3 Continued...
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B. Translating f(x)=3x5 up four units.
New Function:
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Let g(x) be the indicated transformation of f(x). Write the rule for g(x).C. Linear function defined in the table; reflection across yaxis
Step 1: Write the rule for f(x) in slopeintercept form. x f(x)
1 0
0 21 4
yintercept:
slope:
Step 2: Write the rule for g(x). Reflecting f(x) across the yaxis replaces x with x.
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You try!
Let g(x) be the indicated transformation of f(x). Write the rule for g(x).
1a. f(x)=3x+1; translation 2 units right
1b. linear function defined in the table; a reflection across the xaxis
x 1 0 1
y 1 2 3
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Stretching and Compressing Linear Functions
Let g(x) be a horizontal compression of f(x)=2x1 by a factor of 1/3. Write the rule for g(x), and graph the function.
Horizontally compressing f(x) by a factor of 1/3 replaces each x with (1/b)x where b=1/3.
Example
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You try!
Let g(x) be a vertical compression of f(x)=3x+2 by a factor of 1/4. Write the rule for g(x).
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Combining Transformations of Linear Functions
Let g(x) be a vertical shift of f(x)=x down 2 units followed by a vertical stretch by a factor of 5. Write the rule for g(x).
Step 1: First perform the translation
Step 2: Then perform the stretch
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Practice
Page 28 #'s 16
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Review for Quiz
Page 43 #'s 4,5
Page 44 #'s 9, 10
Page 45 #'s 1216
**Please look over the worksheet from Thursday/Friday to also help in reviewing for the 1.11.3 quiz
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Take 5 Minutes to Review Material Before the Quiz!
When you finish raise your hand and I will bring a worksheet by to you!