Lesson 1 - mckinnon2210mckinnon2210.weebly.com/uploads/2/2/8/4/22843616/un… · Web viewUnit 4...

CC Math 1A Name ________________________________

Unit 4 – FunctionsDay Date Lesson Assignment

Lesson 1 – Now-Next Patterns

Lesson 2 – Input-Output Machines

Lesson 3 – Relations, Domain & Range, Functions

Lesson 4 – Graphing Functions

Lesson 5 – Function Notation

Lesson 6 – Graphs of Real World Situations

Lesson 7 – Interpreting Graphs

Lesson 8 – FRED Functions

Review For Test

Unit 4 Test

Unit 4 Homework Grade:

Common Core Math 1A Name _________________________________Unit 4 – FunctionsUnit 4 Lesson 1: Now-Next Patterns Date: _____________________________

1

Guess My Rule:Ex) 5, 10, 15, 20,… Pattern: ________

START = _____ NOW-NEXT form: __________________

Ex) Start:NOW-NEXT form:

You Try!1) 2, 4, 6, 8,… 2) 3, 6, 12, 24,… 3) 2, -4, -10, -16,…

Start: Start: Start:NOW-NEXT form: NOW-NEXT form: NOW-NEXT form:

4) 4, -12, 36, -108,… 5) Start:NOW-NEXT form:

Start:NOW-NEXT form:

What if you were given shapes instead?

Ex)

You Try! 6)

Calculators can quickly iterate (or make) sequences!

Ex. Find the first 5 terms of the sequence for NEXT = 5NOW + 10 when the initial value is 1.2

Now we are going to use this information to write a formal

equation.

Steps: Start by entering your _______ _______. Press _____ _______ 5 _____ _____ + 10 ________ repeatedly

Ex. List the first six values generated by the recursive routine below. Then write the routine as a NOW-NEXT equation.-32.1 EnterAns + 11.8 Enter, Enter, …

You Try!

7) Find the first 5 terms of the sequence for NEXT = -6·NOW + 12 when the initial value is 2.

8) List the first six values generated by the recursive routine below. Then write the routine as a NOW-NEXT equation.54 EnterAns - 9 Enter, Enter, …

Find the dependent values and write the NOW-NEXT equation.

3

Ex1. Ex2.

NOW-NEXT Equation: _____________________ NOW-NEXT Equation: ___________________

You Try! Fill in the points together…

a)

NOW-NEXT Equation:

________________________

b)

NOW-NEXT Equation:

Common Core Math I A Name ________________________________Unit 3 Homework

Day 1 Homework1) Consider the sequence of figures below made from triangles.

4

Term Value01234

Term Value01234

Term Value01234

Term Value01234

a) Complete the table below for the first five figures.Figure

Number Perimeter

1 3

2 5

3

4

5

b) Write a NOW-NEXT equation to find the perimeter of each figure.c) Find the perimeter of the 10th figure.d) Which number figure has a perimeter of 51?

2) List the first six values generated by the recursive routine below. Then write the routine as a NOW-NEXT equation.

3) Write a NOW-NEXT equation for each sequence. Then use your equation to find the 8th term of each sequence.

a) 7.8, 3.6, -0.6, -4.8, . . .

b) -9.2, -6.5, -3.8, -1.1, . . .

c) 1, 3, 9, 27, . . .

d) 36, 12, 4, 43 , . .

Day 1 Homework

5

1) Solve each equation. Show all work!

2) For each of the graphs below, fill in the table of values and write the NOW-NEXT equation for each relationship.

Equation: ___________ ___________ __________ ___________

3) One hundred meter sticks are used to outline a rectangle. Write a recursive routine that generates a sequence of ordered pairs (l, w) that lists all possible rectangles.

4) Match the iterative routine in the first column with the equation in the second column.

Check Understanding Name _______________________________

6

1) START = 0.75NEXT = NOW +2

2) START = -0.75NEXT = NOW +2

3) START = 0.75NEXT = NOW – 2

4) START = -0.75NEXT = NOW – 2

5) START = 2NEXT = NOW – .75

6) START = -2NEXT = NOW – .75

7) START = 2NEXT = NOW + .75

8) START = -2NEXT = NOW + .75

1. Write a NEXT/NOW equation for the sequence 27, 9, 3, 1, 1/3, …

Start: _________

Equation: _________________

2. Using your calculator to find the first 6 terms of the sequence when the initial value is 3 and NEXT=-4NOW-8

______, _______, _______, _______, ________, _________

3. Find the explicit rule of the input/output values and what the output value is when the input is 20.

Rule: _________________________

Output Value: _________

R

Common Core Math 1A Name _________________________________7

x y

1 6

2 12

3 18

4 24

2-3

Output= 3(input)+2

Output

input

157 Output=

__________

61012

Output

input

Unit 4 – FunctionsUnit 4 Lesson 2: Input & Output Machines Date: _____________________________Vocabulary:

___________: A value that is entered

Number going into the machine

___________: A value that is calculated from the input using a set rule

Number that comes out

Finding the OutputFunction rule: input+3=output

Examples:

1. Input = 9 Output = _____

2. Input = 6 Output = _____

How you will see it:

You Try:

Find the rule given the output numbers:

8

You Try: (Same directions, just tables)

1. 2.

Input Output

-3 9

2 -6

4 -12

Rule: __________________ Rule: ____________________

Challenge:

Input Output

1 7

2 9

3 11

4 13

5 15

Rule: ___________________

9

-234 Output=

__________

-468

Output

input

Input Output

6 3

8 4

16 8

More Vocab:

_____________________: an equation that tells how to calculate an output value based on a given input value

How is this different from recursive?

Explicit formula examples:

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1. Find the explicit equation then find what the output value would be when the input is 15.

Directions: Find the explicit equation and output value when the input is 25.

2. 3.

Input: ____ value

Output: ____ value

Rule!

Now instead of using Input and Output . . .

11

1

4

9

-11-22-33

01-12-2

012

Day 2 Homework: Input-Output Machine

Our input-output machine takes a number [x], operates on the number, and changes it to a new number [y]. Below are some input-output machines, the input [x], and the output [y]. Can you figure out the rule for what the machine did to the input?

5. Here is a corner of a coding grid.a. Does each input letter code to a single output?b. Does each output letter decode to a single input?c. If this code were a function, which would be made easier, coding or decoding?

Explain.d. How would you change this grid to make it a function?

6. For each diagram, give the input values and output values and then tell whether or not each relationship is a function. Explain why or why not.

a. b.

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DCBA

A B C D

Common Core Math 1A Name _________________________________Unit 4 – FunctionsUnit 4 Lesson 3: Relations, Domain & Range, Functions Date: _____________________________

13

Common Core Math 1A Name _________________________________Unit 4 – FunctionUnit 4 Lesson 4: Graphing Functions Date: _____________________________

23

Common Core Math 1A Name _________________________________Unit 4 – FunctionsUnit 4 Lesson 5: Function Notation Date: _____________________________

27

2 4 6 8 10 12 14 16Time (hrs)

Depth (ft)1 2 3 4

Common Core Math 1A Name _________________________________Unit 4 – FunctionsUnit 4 Lesson 6: Graphs of Real-World Situations Date: _____________________________

Graphs of Real-World SituationsIn this lesson you will

● describe graphs using the words increasing, decreasing, linear, and nonlinear● match graphs with descriptions of real-world situations● learn about continuous and discrete functions● use intervals of the domain to help you describe a function’s behavior

Like pictures, graphs communicate a lot of information. So you need to be able to draw and make sense of graphs. In Unit 1, you learned to interpret dotplots, histograms, and boxplots based on one quantity. In this lesson you’ll look at graphs that show how two real-world quantities are related, and you’ll practice interpreting and describing graphs.

Investigation: Interpreting GraphsThis graph shows the relationship between time and the depth of water in a leaky swimming pool.

What is the initial depth of the water?

For what time interval(s) is the water level decreasing? What accounts for the decrease(s)?

For what time interval(s) is the water level increasing? What accounts for the increase(s)?

Is the pool ever empty? How can you tell?

In this example, the depth of the water is a function of time. That is, the depth depends on how much time has passed. So, in this case, depth is called the dependent variable. Time is the independent variable. When you draw a graph, put the independent variable on the x-axis and put the dependent variable on the y-axis.

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On the graph of this function, you can see the domain values that are possible for the independent variable in this real-world context. This is called the practical domain. The practical domain in this example is the set of all instants of time from 0 to 16 hours. We can express this as 0≤ x≤ 16, where x is the independent variable representing time.

You can also see the values that are possible for the dependent variable. In this example the range is the set of all numbers between 1 ft and about 3.3 ft. We can express this as 1 ≤ y ≤3.3, where y is the dependent variable representing the depth of the water in feet. Notice that the lowest value for the range (1 ft) does not have to be the starting value when x is zero (2 ft).

The relationship between the independent and dependent variable is not always a cause and effect relationship. In many situations, time is the independent variable. It is the independent variable in graphs such as population growth or car depreciation and in several relationships of the form (time, distance). But time does not cause a population to grow or a walker’s distance from a given point to change. People do that.

The values of the range depend on the values of the domain. If you know the value of the independent variable, you can determine the corresponding value of the dependent variable. You do this every time you locate a point on the graph of a function.

This graph shows the volume of air in a balloon as it changes over time.

What is the independent variable? How is it measured?

What is the dependent variable? How is it measured?

For what intervals is the volume increasing? What accounts for the increases?

For what intervals is the volume decreasing? What accounts for the decreases?

For what intervals is the volume constant? What accounts for this?

What is happening for the first 2 seconds?

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y

x

y

x

y

x

y

x

y

xx

y

x

y

x

Investigation: Matching UpThe graphs below show increasing functions, meaning that as the x-values increase, the y-values also increase. In Graph A, the function values increase at a constant rate. In Graph B, the values increase slowly at first and then more quickly. In Graph C, the function switches from one constant rate of increase to another.

The graphs below show decreasing functions, meaning that as the x-values increase, the y-values decrease. In Graph D, the function values decrease at a constant rate. In Graph E, the values decrease quickly at first and then more slowly. In Graph F, the function switches from one constant rate of decrease to another.

The graphs below show functions that have both increasing and decreasing intervals. In Graph G, the function values decrease at a constant rate at first and then increase at a constant rate. In Graph H, the values increase slowly at first and then more quickly and then begin to decrease quickly at first and then more slowly. In Graph I, the function oscillates between two values.

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Graph A Graph B Graph C

Graph D Graph E Graph F

x Graph G Graph H Graph I

Read the description of each situation below. Identify the independent and dependent variables. Then decide which of the graphs above match the situation.

White Tiger PopulationA small group of endangered white tigers are brought to a special reserve. The group of tigers reproduces slowly at first, and then as more and more tigers mature, the population grows more quickly.

Independent Variable:

Dependent Variable:

Matching Graph:

Temperature of Hot TeaGrandma pours a cup of hot tea into a tea cup. The temperature at first is very hot, but cools off quickly as the cup sits on the table. As the temperature of the tea approaches room temperature, it cools off more slowly.


Dependent Variable:

Matching Graph:

Number of Daylight Hours over a Year’s TimeIn January, the beginning of the year, we are in the middle of winter and the number of daylight hours is at its lowest point. Then the number of daylight hours increases slowly at first through the rest of winter and early spring. As summer approaches, the number of daylight hours increases more quickly, then levels off and reaches a maximum value, then decreases quickly, and then decreases more slowly into fall and early winter.


Dependent Variable:

Matching Graph:

Height of a Person Above Ground Who is Riding a Ferris WheelWhen a girl gets on a Ferris wheel, she is 10 feet above ground. As the Ferris wheel turns, she gets higher and higher until she reaches the top. Then she starts to descend until she reaches the bottom and starts going up again.

Independent Variable: Matching Graph:

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y

x

y

x

y

x

y

x

y

x

y

x

y

x

y

x

Dependent Variable:

Investigation: Discrete vs. ContinuousFunctions that have smooth graphs, with no breaks in the domain or range, are called continuous functions. Functions that are not continuous often involve quantities—such as people, cars, or stories of a building—that are counted or measured in whole numbers. Such functions are called discrete functions. Below are some examples of discrete functions.

Match each description with its most likely graph. Then label the axes with the appropriate quantities.

a) the amount of product sold vs. advertising budgetb) the amount of a radioactive substance over timec) the height of an elevator relative to floor numberd) the population of a city over timee) the number of students who help decorate for the homecoming dance vs. the time

it takes to decorate

Sort the following key terms into two groups. Then draw lines connecting pairs of terms that go together (one from each group).

dependent, distance, horizontal axis, independent, input, output, time, vertical axis, x, y

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Graph 1 Graph 2 Graph 3

Graph 4 Graph 5

1) For each relationship, identify the independent variable and the dependent variable.

a. The temperature of a carton of milk and the length of time it has been out of the refrigerator.

b. the weight suspended from a rubber band the length of the rubber band.

c. the diameter of a pizza and its cost.

d. The number of privately owned cars and the standard of living in a country.

e. The number of cars on the freeway and the level of exhaust fumes in the air.

2) Sketch a reasonable graph for each situation and label the axes.

a. The temperature of a pot of water as it is heated

b. The relationship between the cooking time for a 2-pound roast and the temperature of the oven

c. The distance from a Ferris-wheel rider to the ground during two revolutions

3. Match each description with its most likely graph, and tell which variable each axis represents.

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a. The relationship between your grade on the next math test and the amount of time you spend doing math problems before the test

b. The relationship between the amount a person earns in an 8-hour day and his or her hourly wagec. The change in the area of a square as its side length increases

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Common Core Math 1A Name _________________________________Unit 4 –FunctionsUnit 4 Lesson 7: Interpreting Graphs Date: _____________________________

Interpreting GraphsIn this lesson you will continue to

describe graphs using the words increasing, decreasing, linear, and nonlinear

match graphs with descriptions of real-world situationsYou will also

use intervals of the domain to help you describe a function’s behavior write a description of a real-world relationship displayed in a graph draw a graph to match a description of a real-world situation

Every day we are bombarded with information, often in graph form. To “read” a graph, you have to understand how the quantities in the graph relate to each other, how they make the graph go up or down or level off. The function values in a graph can change at a constant rate or at a varying rate as the x-values of a function increase steadily.

In this lesson you’ll look at graphs that show how two real-world quantities are related.

Investigation: Matching UpA function is linear if, as x changes at a constant rate, the function values change at a constant rate. The graphs of linear functions appear as straight lines. A function is nonlinear if, as x changes at a constant rate, the function values change at a varying rate. The graphs of non-linear functions are curved.

Which graphs below are linear?

Which graphs are nonlinear?

Which graphs are increasing?

Which graphs are decreasing?

Are there any graphs that are neither increasing nor decreasing? or both? Explain.

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In order to describe the relationship pictured on a graph, it often help to break the domain into intervals where the graph is increasing, decreasing, or constant.

EXAMPLE Use the intervals marked on the x-axis in the graph below to help you discuss where the function is increasing or decreasing and where it is linear or nonlinear. The first interval is done for you.

Interval 1: 0 ≤ x≤ 3 The function is decreasing in the interval 0 ≤ x≤ 6. In the interval 0 ≤ x≤ 3, the function is nonlinear and decreases slowly at first and then more quickly.

Interval 2:

Interval 3:

Interval 4:

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Graph G Graph H

Investigation: Describing GraphsConsider the following scenario:

A turtle crawls steadily from its pond across the lawn. Then a small dog picks up the turtle and runs with across the lawn. The dog slows down and finally drops the turtle. The turtle rests for a few minutes after this excitement. Then a young girl comes along, picks up the turtle, and slowly carries it back to the pond.

Which of the graphs depicts the turtle’s distance from the pond over time? Explain.

Select one of the other three graphs. Work with your partner to write a story that would be depicted by the graph. (You can use the turtle or another situation.)

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Investigation: Sketch a GraphRead the following story about a volleyball game.

Before a volleyball game starts, the people that can be found in the school gym are the players, coaches, and the people working the event (ticket takers, officials, scorers, etc.) Slowly the fans arrive for the match. Just before the first game, the people are coming in as fast as the tickets can be sold. After the match is over, most of the parents and fans leave. Then more students arrive for the after-game dance. Most of the students leave after an hour. The people that remain are the ones who have been working at the gym all night long.

What is the independent variable for this situation?

What are reasonable values for the domain? Are they positive or negative numbers? Whole numbers or decimals?

What is the dependent variable?

What are reasonable values for the domain? Are they positive or negative numbers? Whole numbers or decimals?

Sketch a graph that matches the story. Be sure to label the axes.

Is your graph discrete or continuous? Explain why you drew it that way.

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0 2 4 6 8 10 12 14 16 18 20 22 24

A B C D E

y

x

y

x

y

x

y

x

Compare your graph to your partner’s graph. How are they alike? How are they different? Are both graphs reasonable?

1) Sketch a graph of a continuous function to fit each description.

a) always increasing with a faster and faster rate of change

b) decreasing with a slower and slower rate of change, then increasing with a faster and faster rate of change

c) linear and decreasing

d) decreasing with a faster and faster rate of change

2) Write an inequality for each interval. Include the least point in each interval and exclude the greatest point in each interval.

a) AB

b) BC

c) CD

d) DE

3) Describe each of these discrete function graphs using the words increasing, decreasing, linear, nonlinear, and rate of change.

a) b) c) d)

4) Sketch a discrete function graph to fit each description.

a) always increasing with a slower and slower rate of change

b) linear with a constant rate of change equal to zero

c) linear and decreasing

d) decreasing with a faster and faster rate of change

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8:00 10:00 12:00Time

Blood Pressure

12 4 8 12 4 8 12 Time

Temperatu

re

5) This graph shows Anne’s blood pressure level during a morning at school. Give the points or intervals when her blood pressure . . .

a) reached its highest point.

b) was rising the fastest.

c) was decreasing.

6) This graph shows the air temperature in a 24-hr period from midnight to midnight. Write a description of this graph, giving the intervals as the temperature changed.

7) For each relationship identify the independent and dependent variables.

a) the mass of a spherical lollipop and the number of times it has been licked.

b) the number of scoops in an ice cream cone and the cost of the cone.

c) the distance a rubber band will fly and the amount you stretch it before you release it.

d) the number of coins you flip and the number of heads.

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F(x)

Common Core Math 1A Name _________________________________Unit 4 – FunctionsUnit 4 Lesson 8: FRED Functions Date: _____________________________

Transformations with Fred Functions – Day 1

To the right is a graph of a “Fred” function. We can use Fred functions to explore transformations in the coordinate plane.

I. Let’s review briefly.

1. a. Explain what a function is in your own words.

b. Using the graph, how do we know that Fred is a function?

2. a. Explain what we mean by the term domain.

b. Using the graph, what is the domain of Fred?

3. a. Explain what we mean by the term range.

b. Using the graph, what is the range of Fred?

4. Let’s explore the points on Fred.a. How many points lie on Fred? Can you list them all?

b. What are the key points that would help us graph Fred?

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We are going to call these key points “characteristic” points. It is important when graphing a function that you are able to identify these characteristic points.

c. Use the graph of graph to evaluate the following.

F(1) = _____ F( –1) = _____ F(_____) = –2 F(5) = ______II.

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Remember that F(x) is another name for the y-values.

Therefore the equation of Fred is y = F(x).

x F(x)–1

1

2

4

1. Why did we choose those x-values to put in the table?

Now let’s try graphing Freddie Jr.: y = F(x) + 4. Complete the table below for this new function and then graph Freddie Jr. on the coordinate plane above.

y = F(x) + 4x y

–1

1

2

4

2. What type of transformation maps Fred, F(x), to Freddie Jr., F(x) + 4? (Be specific.)

3. How did this transformation affect the x-values? (Hint: Compare the characteristic points of Fred and Freddie Jr.)

4. How did this transformation affect the y-values? (Hint: Compare the characteristic points of Fred and Freddie Jr.)

5. In y = F(x) + 4, how did the “+4” affect the graph of Fred? Did it affect the domain or the range?III.

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III. Suppose Freddie Jr’s equation is: y = F(x) – 3. Complete the table below for this new function and then graph Freddie Jr. on the coordinate plane above.

y = F(x) – 3x y

–1

1

2

4

1. What type of transformation maps Fred, F(x), to Freddie Jr., F(x) – 3? Be specific.



4. In y = F(x) – 3, how did the “– 3” affect the graph of Fred? Did it affect the domain or the range?

IV. Checkpoint: Using the understanding you have gained so far, describe the affect to Fred for the following functions.

Equation Effect to Fred’s graphExample: y=F(x) +

18Translate up 18 units

1. y = F(x) – 100

2. y = F(x) + 73

3. y = F(x) + 32

4. y = F(x) – 521

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V. Suppose Freddie Jr’s equation is: y = F(x + 4).

1. Complete the table.

x x + 4 Y

–5 –1 1

1 –1

2 –1

4 –2

(Hint: Since, x + 4 = –1, subtract 4 from both sides of the equation, and x = –5. Use a similar method to find the missing x values.)

2. On the coordinate plane above, graph the 4 ordered pairs (x, y). The first point is (–5, 1).

3. What type of transformation maps Fred, F(x), to Freddie Jr., F(x + 4)? (Be specific.)



6. In y = F(x + 4), how did the “+4” affect the graph of Fred? Did it affect the domain or the range?

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VI. Suppose Freddie Jr’s equation is: y = F(x – 3). Complete the table below for this new function and then graph Freddie Jr. on the coordinate plane above.

1. Complete the table.

y = F(x – 3)x x – 3 y

–1

1

2

4

2. On the coordinate plane above, graph the 4 ordered pairs (x, y). [Hint: The 1st point should be (2, 1).]

3. What type of transformation maps Fred, F(x), to Freddie Jr., F(x – 3)? (Be specific.)



6. In y = F(x – 3), how did the “ –3” affect the graph of Fred? Did it affect the domain or the range?

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VII. Checkpoint: Using the understanding you have gained so far, describe the effect to Fred for the following functions.

Equation Effect to Fred’s graph

Example: y=F(x + 18) Translate left 18 units

1. y = F(x – 10)

2. y = F(x) + 7

3. y = F(x + 48)

4. y = F(x) – 22

5. y = F(x + 30) + 18

VIII. Checkpoint: Using the understanding you have gained so far, write the equation that would have the following effect on Fred’s graph.


Example: y=F(x + 8) Translate left 8 units

1. Translate up 29 units

2. Translate right 7

3. Translate left 45

4. Translate left 5 and up 14

5. Translate down 2 and right 6

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IX. Now let’s look at a new function. Its notation is H(x), and we will call it Harry.Use Harry to demonstrate what you have learned so far about the transformations of functions.

1. What are Harry’s characteristic points?

__________________________________________

2. Describe the effect on Harry’s graph for each of the following.a. H(x – 2) _______________________________________________

b. H(x) + 7 _______________________________________________

c. H(x+2) – 3 _______________________________________________

3. Use your answers to questions 1 and 2 to help you sketch each graph without using a table.

a. y = H(x – 2) b. y = H(x) + 7

c. y = H(x+2) – 3

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Transformations with Fred – Day 1 Practice Name ________________________

I. On each grid, Ginger, G(x) is graphed. Graph the given function.

1. Graph: y = G(x) – 6. 2. Graph: y = G(x + 6)2.

3. Graph: y = G(x + 2) + 5 4. Graph: y = G(x – 4) – 5

II. Using the understanding you have gained so far, describe the effect to Fred for the following functions.

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1. y = F(x) + 82

2. y = F(x – 13)

3. y = F(x + 9)

4. y = F(x) – 55

5. y = F(x – 25) + 11

III. Using the understanding you have gained so far, write the equation that would have the following effect on Fred’s graph.


6. Translate left 51 units

7. Translate down 76

8. Translate right 31

9. Translate right 8 and down 54

10. Translate down 12 and left 100

IV. Determine the domain and range of each parent function.

1. Harry, H(x) 2. Ginger, G(x)

Domain: ____________________ Domain: ____________________

Range: ____________________ Range: ____________________

V. Consider a new function, Polly, P(x). Polly’s Domain is { x|−2≤ x≤ 2}. Its range is { y|−3≤ y ≤1 }.

Use your understanding of transformations of functions to determine the domain and range of each of the following functions. (Hint: You may want to write the effect to Polly first.)

1. P(x) + 5 2. P(x + 5)

Domain: _________________________ Domain:

___________________________

Range: ________________________ Range: ___________________________

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1) Describe each translation:Parent

FunctionTranslated Function

a)

y=|x| y=|x+4|

b)

y=12

x−6 y=12

( x−4 )−6

c) y=x2 y=(x−2)2−3

d)

y=|x| y=1+|x−3|

e) y=x2+7 y=(x+4)2+7

f) y=−34

x+1 y=−34

x+8

2) Write the function t (x) for each of these transformations:a) Translate the graph of f (x)=x2 right 3 units.b) Translate the graph of f (x)=|x| left 5 units.c) Translate the graph of f ( x )=2x−7 right 2 units.d) Translate the graph of f (x)=x2 up 3 units.e) Translate the graph of f (x)=|x| down 4 units.f) Translate the graph of f ( x )=−3 x+2left 2 units and up 3 units.

3) Is the following function a translation 5 units right or 5 units down? ExplainParent function: f ( x )=x Translated function: t ( x )=x−5

4) Below are tables of points for two functions. Describe the transformation.Parent function Translated

functionx y x y

−1 3 7 −1

3 5 11 12 4 10 0

5) Describe each transformation. Then write an equation for t (x) in terms of f (x).

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a) b)

6) This graph show’s Beth’s distance from her teacher as she turns in her test.a) What are the input and output variables?b) What are the units for each variable?c) What are the domain and range shown in the graph?d) Give a story describing the graph in context.e) Challenge: This graph is a translation of the absolute value function. Write a function that models this situation.

7) Graph the parent graph Y1(X) = abs(X) on your graphing calculator. For each of the following, predict what each graph will look like. Then check by graphing each function.

a) Y2(X) = Y1(X) – 4 b) Y2(X) = Y1(X – 4)

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f (x)

t (x)

f (x)

t (x)

Time (sec)

Dist

ance

from

Tea

cher

(m)

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