Algebra 1 4-6 Complete Lesson: Formalizing Relations and Functions

Last updated about 4 years ago

31 questions

Note from the author:

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Library

Algebra 1 4-6 Complete Lesson: Formalizing Relations and Functions

Last updated about 4 years ago

31 questions

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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F.IF.1

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Problem 1 Got It? Represent the relation with a mapping diagram.

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Problem 1 Got It? Represent the relation with a mapping diagram.

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5

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Problem 3 Got It? Use the function in Problem 3, w(x) = 250x. How many words can you read in 6 min? Enter only a number.

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F.IF.1

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Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

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20

Compare and Contrast: You can use a mapping diagram or the vertical line test to tell if a relation is a function. Which method do you prefer? Explain.

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Error Analysis: A student drew the dashed line on the graph shown and concluded that the graph represented a function. Is the student correct? Explain.

F.IF.1

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30

Review Lesson 4-1: Describe how the variables are related at the indicated points on the graph.

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100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

10

Reflection: Math Success

F.IF.1

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Problem 1 Got It? Identify the domain and range of the relation.
Place each value only once.

4.2
1.5
5
2.2
7
4.8
0

Domain
Range

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Is the relation a function?

Yes

No

Problem 1 Got It? Identify the domain and range of the relation.
Place each value only once.

-1
1
-2
2
4
-4
7
-7

Domain
Range

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Is the relation a function?

Yes

No

5

F.IF.1

5

F.IF.1

10

Problem 3 Got It? Use the function in Problem 3, w(x) = 250x. How many words can you read in 6 min? Enter only a number.

10

F.IF.1

10

F.IF.1

5

F.IF.1

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the domain of the relation.

{-3, -2, -1, 0, 1, 5, 6}

{-3, 4, 5, 6}

{-2, -1, 0, 1}

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the range of the relation.

{-2, -1, 0, 1}

{-3, 4, 5, 6}

{-3, -2, -1, 0, 1, 5, 6}

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

5

F.IF.1

What is f(2) for the function f(x) = 4x + 1?

43

-2

9

3

The domain of f(x), defined below, is {-4, -2, 0, 2, 4}. What is the range?

{-8, -4, 0, 4, 8}

{-2, -1, 0, 1, 2}

{-2, -1, 1, 2}

Vocabulary: Write y = 2x + 7 using function notation.

f(x) = {y|y is a Real number, y = 2x + 7}

f(x) = 2x + 7

Compare and Contrast: You can use a mapping diagram or the vertical line test to tell if a relation is a function. Which method do you prefer? Explain.

10

Error Analysis: A student drew the dashed line on the graph shown and concluded that the graph represented a function. Is the student correct? Explain.

F.IF.1

Review Lesson 4-5: Match each function rule with the situation it models.

E = 7 + 5h
a = 4.5s + 10

You buy several pairs of socks for $4.50 per pair, plus a shirt for $10. The total amount a you spend is a function of the number of pairs of socks you buy.
You babysit for $5 per hour and get a $7 tip. Your earnings E are a function of the number of hours h you work.

10

Review Lesson 4-1: Describe how the variables are related at the indicated points on the graph.

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4.

x = 1
x = 2
x = 3
x = 4

Expression = 18
Expression = 12
Expression = 9
Expression = 15

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4. Only use each x-value once.
Not all expression value categories will be used.

x = 1
x = 2
x = 3
x = 4

Expression = 7
Expression = 15
Expression = 29
Expression = 22
Expression = 8

Vocabulary Review: Use the words in the left column to label the function machine in the image below. Use each word once.

function rule
y-values
output
x-values
input
range

Region A
Region B
Region C

Use Your Vocabulary: Complete each sentence with the appropriate word from the column on the left. Use each word once.

reasonable
reasonableness
unreasonable

The student estimated to check the __?__ of her answer.
Sales tax of $32 on an $85 item is __?__.
A price of $14 is __?__ for a pizza.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! Your friend is playing a board game. He is on the space shown in the diagram. He rolled a 3 to get to that space. On which spaces could he have started before rolling the 3? Select all that apply.

Problem 1 Got It? Identify the domain and range of the relation. 
Place each value only once.

4.2

1.5

5

2.2

7

4.8

0

Domain

Range

Problem 1 Got It? Is the relation a function?

Yes

No

Problem 1 Got It? Identify the domain and range of the relation. 
Place each value only once.

-1

1

-2

2

4

-4

7

-7

Domain

Range

Problem 1 Got It? Is the relation a function?

Yes

No

Problem 2 Got It?

A

B

Problem 2 Got It?

A

B

Problem 4 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Problem 5 Got It?

A

B

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the domain of the relation.

{-3, -2, -1, 0, 1, 5, 6}

{-3, 4, 5, 6}

{-2, -1, 0, 1}

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the range of the relation.

{-2, -1, 0, 1}

{-3, 4, 5, 6}

{-3, -2, -1, 0, 1, 5, 6}

Is the relation in the graph a function? Use the vertical line test.

Yes, it is a function.

No, it is not a function.

What is f(2) for the function f(x) = 4x + 1?

43

-2

9

3

The domain of f(x), defined below, is {-4, -2, 0, 2, 4}. What is the range?

{-8, -4, 0, 4, 8}

{-2, -1, 0, 1, 2}

{-2, -1, 1, 2}

Vocabulary: Write y = 2x + 7 using function notation.

f(x) = {y|y is a Real number, y = 2x + 7}

f(x) = 2x + 7

Review Lesson 4-5: Match each function rule with the situation it models.

E = 7 + 5h

a = 4.5s + 10

You buy several pairs of socks for $4.50 per pair, plus a shirt for $10. The total amount a you spend is a function of the number of pairs of socks you buy.

You babysit for $5 per hour and get a $7 tip. Your earnings E are a function of the number of hours h you work.

Review Lesson 4-1: The graph shows a family's distance from home as they drive to the mountains for a vacation. Label the variables in the graph.

variable

Number of trips
Time
Elevation
Number of deer spotted
Distance from home

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4.

x = 1

x = 2

x = 3

x = 4

Expression = 18

Expression = 12

Expression = 9

Expression = 15

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4. Only use each x-value once.
Not all expression value categories will be used.

x = 1

x = 2

x = 3

x = 4

Expression = 7

Expression = 15

Expression = 29

Expression = 22

Expression = 8

Vocabulary Review: Use the words in the left column to label the function machine in the image below. Use each word once. 

function rule

y-values

output

x-values

input

range

Region A

Region B

Region C

Use Your Vocabulary: Complete each sentence with the appropriate word from the column on the left. Use each word once.

reasonable

reasonableness

unreasonable

The student estimated to check the __?__ of her answer.

Sales tax of $32 on an $85 item is __?__.

A price of $14 is __?__ for a pizza.

Solve It! Your friend is playing a board game. He is on the space shown in the diagram. He rolled a 3 to get to that space. On which spaces could he have started before rolling the 3? Select all that apply.

Problem 2 Got It?

A

B

Problem 2 Got It?

A

B

Problem 4 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Problem 5 Got It?

A

B

Is the relation in the graph a function? Use the vertical line test.

Yes, it is a function.

No, it is not a function.

Review Lesson 4-1: The graph shows a family's distance from home as they drive to the mountains for a vacation. Label the variables in the graph.

variable

Number of trips

Time

Elevation

Number of deer spotted

Distance from home

Algebra 1 4-6 Complete Lesson: Formalizing Relations and Functions

Algebra 1 4-6 Complete Lesson: Formalizing Relations and Functions

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 3 Got It? Use the function in Problem 3, w(x) = 250x. How many words can you read in 6 min? Enter only a number.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

Compare and Contrast: You can use a mapping diagram or the vertical line test to tell if a relation is a function. Which method do you prefer? Explain.

Error Analysis: A student drew the dashed line on the graph shown and concluded that the graph represented a function. Is the student correct? Explain.

Review Lesson 4-1: Describe how the variables are related at the indicated points on the graph.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 1 Got It? Identify the domain and range of the relation. Place each value only once.

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Is the relation a function?

Problem 1 Got It? Identify the domain and range of the relation. Place each value only once.

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Is the relation a function?

Problem 3 Got It? Use the function in Problem 3, w(x) = 250x. How many words can you read in 6 min? Enter only a number.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.Identify the domain of the relation.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.Identify the range of the relation.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

What is f(2) for the function f(x) = 4x + 1?

The domain of f(x), defined below, is {-4, -2, 0, 2, 4}. What is the range?

Vocabulary: Write y = 2x + 7 using function notation.

Compare and Contrast: You can use a mapping diagram or the vertical line test to tell if a relation is a function. Which method do you prefer? Explain.

Error Analysis: A student drew the dashed line on the graph shown and concluded that the graph represented a function. Is the student correct? Explain.

Review Lesson 4-5: Match each function rule with the situation it models.

Review Lesson 4-1: Describe how the variables are related at the indicated points on the graph.

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4.

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4. Only use each x-value once.Not all expression value categories will be used.

Vocabulary Review: Use the words in the left column to label the function machine in the image below. Use each word once.

Use Your Vocabulary: Complete each sentence with the appropriate word from the column on the left. Use each word once.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! Your friend is playing a board game. He is on the space shown in the diagram. He rolled a 3 to get to that space. On which spaces could he have started before rolling the 3? Select all that apply.

Problem 2 Got It?

Problem 2 Got It?

Problem 4 Got It?

Problem 5 Got It?

Problem 5 Got It?

Is the relation in the graph a function? Use the vertical line test.

Review Lesson 4-1: The graph shows a family's distance from home as they drive to the mountains for a vacation. Label the variables in the graph.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Problem 1 Got It? Identify the domain and range of the relation.
Place each value only once.

Problem 1 Got It? Identify the domain and range of the relation.
Place each value only once.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the domain of the relation.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the range of the relation.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4. Only use each x-value once.
Not all expression value categories will be used.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.