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Algebra I: Algebra I: Algebra I: Algebra I: Week Week Week Week 26 Math Packet Math Packet Math Packet Math Packet March 7 th – March 11 th Unit 8: Transforming Functions & Modeling *Week 26 HW: Finish Angry Birds Project by Week 26 HW: Finish Angry Birds Project by Week 26 HW: Finish Angry Birds Project by Week 26 HW: Finish Angry Birds Project by Thursday Thursday Thursday Thursday

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Page 1: Algebra I:Algebra I: Week Week Week 22226666 …mangicaroywcp.weebly.com/uploads/3/0/4/3/30436700/week26...i. U > 1 iv. −1

Algebra I:Algebra I:Algebra I:Algebra I: Week Week Week Week 22226666 Math PacketMath PacketMath PacketMath Packet March 7th – March 11th

Unit 8: Transforming Functions & Modeling

****Week 26 HW: Finish Angry Birds Project by Week 26 HW: Finish Angry Birds Project by Week 26 HW: Finish Angry Birds Project by Week 26 HW: Finish Angry Birds Project by ThursdayThursdayThursdayThursday

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

1

Jump StartJump StartJump StartJump Start

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

2

Graphing Cubic, Square Root, and Cube Root FunctionsGraphing Cubic, Square Root, and Cube Root FunctionsGraphing Cubic, Square Root, and Cube Root FunctionsGraphing Cubic, Square Root, and Cube Root Functions

Example 1: Use your graphing calculator to create a data table for the functions 4 5 67 and 4 5 √6

for a variety of 6-values. Use both negative and positive numbers, and round decimal answers to the

nearest hundredth.

9 : 5 9; : 5 √9

4

2

0

-2

-4

Use the table above and your calculator to participate in the discussion using the questions below.

a) What do you notice about the values in the two y-columns?

b) Why are all the y-values for y = x2 positive?

c) Why do all the negative x-values produce an error for 4 5 √6?

d) What is the domain of 4 5 67 and 4 5 √6?

e) What is the range of 4 5 67 and 4 5 √6

f) Create the graphs of 4 5 67 and 4 5 √6 on

the same set of axes to the right.

g) How are the graphs related to each other?

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

3

Example 2: Create a data table for 4 5 6= and 4 5 √6>, and graph both functions on the same set of

axes. Round decimal answers to the nearest hundredth.

a) What is the domain and range for each function?

b) What is the relationship between the two functions?

9 : 5 9? : 5 √9?

−8

−2

−1

0

1

2

8

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

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Independent Practice Independent Practice Independent Practice Independent Practice

1. Create the graphs of the functions CD6E 5 67 F 2 and GD6E 5 √6 F 2 using the given values. Use

a calculator to help with decimal approximations.

9 HD9E ID9E

−4

−2

−1

0

1

2

4

2. What is the domain and range for each function?

3. Describe the relationship between the graphs given by the equations 4 5 67 F 2 and

4 5 √6 F 2. How are they alike? How are they different?

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

5

Translating FunctionsTranslating FunctionsTranslating FunctionsTranslating Functions

Example 1: Using your calculator, graph each set of functions on the same coordinate plane and

explain what similarities and differences you see.

a. C(6) 5 67

G(6) 5 67 F 3

ℎ(6) 5 67 − 7

b. C(6) 5 |6| G(6) 5 |6 F 3| ℎ(6) 5 |6 − 4|

Jump Jump Jump Jump StartStartStartStart

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

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Example 2: For each graph, answer the following:

� What is the parent function?

� How does the translated graph relate to the graph of the parent function?

� Write the formula for the function depicted by the translated graph.

a.

b.

Translations...Translations...Translations...Translations...

-shift functions up, down, left, or right

*If the parent function is f(x), a translation up or down will occur when a constant, k, is added or

subtracted such that the new function is g(x) = f(x) + k or g(x) = f(x) – k

**If the parent function is f(x), a translation left or right will occur when a constant, k, is added or

subtracted such that the new function is g(x) = f(x + k) or g(x) = f(x – k)

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

7

c.

Independent Practice Independent Practice Independent Practice Independent Practice

1) If f(x) represents the parent function, describe how the translated graphs represented by p(x) and

q(x) relate to the parent function.

CD6E 5 √6

MD6E 5 10 F √6

ND6E 5 √6 F 8

2) Write a function that translates the graph of the parent function CD6E 5 67 down 7.5 units and

right 2.5 units.

3) How would the graph of CD6E 5 |6| be affected if the function were transformed to CD6E 5 |6 F 6| F 10?

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

8

4) Match the correct equation and description of the function with the given graphs.

Graphs Equation Description

4 5 CD6E

Equation _________ Description ___________

E1. 4 5 D6 @ 3E7

E2. 4 5 D6 F 2E7 @ 3

E3. 4 5 @D6 @ 3E7 @ 2

E4. 4 5 D6 @ 2E7 @ 3

D1. The graph of the

parent function is

translated down 3

units and left 2 units.

D2. The graph of the

function does not

have an 6-intercept.

D3. The coordinate of

the 4-intercept is

D0, 1E, and both 6-

intercepts are

positive.

D4. The graph of the

function has only

one 6-intercept.

4 5 GD6E

Equation _________ Description ___________

4 5 KD6E

Equation _________ Description ___________

4 5 MD6E

Equation _________ Description ___________

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

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Jump StartJump StartJump StartJump Start

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

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Stretching and ShrinkingStretching and ShrinkingStretching and ShrinkingStretching and ShrinkingFunctions Functions Functions Functions

Example 1: Complete the following table of values for each transformation of the function C. Then,

graph the equations on your calculator. Let f(x) = x2 be the parent function.

9 HD9E ID9E 5 ?HD9E PD9E 5 ;HD9E QD9E 5 R. SHD9E TD9E 5 −;HD9E

@4

−2

0

2

4

Describe how the graph of 4 5 UCD6E relates to the graph of 4 5 CD6E for each case.

i. U > 1 iv. −1 < U < 0

ii. 0 < U < 1 v. U < −1

Vertical Stretching/ShrinkingVertical Stretching/ShrinkingVertical Stretching/ShrinkingVertical Stretching/Shrinking

-a function is stretched/shrunk vertically when the parent function y = f(x) is multiplied by a

constant, k, such that the new function is y = kf(x).

*When k is positive and bigger than 1... *When k is positive and smaller than 1...

*When k is a negative number bigger than -1... *When k is a negative number smaller than -1...

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Example 2: Example 1: Complete the following table of values for each transformation of the function

C. Then, graph the equations on your calculator. Let f(x) = √6> be the parent function.

9 HD9E ID9E 5 HD;9E PD9E 5 HDR. S9E QD9E 5 HD−;9E

@8

−1

0

1

8

Describe how the graph of 4 5 UCD6E relates to the graph of 4 5 CD6E for each case.

i. U > 1 iv. −1 < U < 0

ii. 0 < U < 1 v. U < −1

Horizontal Stretching/ShrinkingHorizontal Stretching/ShrinkingHorizontal Stretching/ShrinkingHorizontal Stretching/Shrinking

-a function is stretched/shrunk horizontally when the parent function y = f(x) is multiplied by a

constant, k, such that the new function is y = f(kx).

*When k is positive and bigger than 1... *When k is positive and smaller than 1...

*When k is a negative number bigger than -1... *When k is a negative number smaller than -1...

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Name: _______________________________________________ Algebra IAlgebra IAlgebra IAlgebra I: Week : Week : Week : Week 26262626 Math PacketMath PacketMath PacketMath Packet Ms. Mangicaro

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Independent Practice Independent Practice Independent Practice Independent Practice

1) If f(x) represents the parent function, describe how the translated graphs relate to the parent

function for each set of functions below.

a. CD6E 5 |6| GD6E 5 4|6| KD6E 5 |26| UD6E 5 @2|26|

b. GD6E 5 √6>

MD6E 5 2√6>

ND6E 5 −2√26>

2) If f(x) = |x| is the parent function, explain how the graphs of functions GD6E 5 3|6| and

ℎD6E 5 |36| are related to the parent function.

3) If f(x) = |x| is the parent function, explain how the graphs of functions ND6E 5 @3|6| and

[D6E 5 | −36| are related the parent function.