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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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COPY CHART BELOW!

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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!

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