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

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by Matthew Richardson

| 31 QuestionsNote 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.

1

1

10 pts

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.

1

2

3

4

5

6

7

8

9

10

2

10 pts

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

3

10 pts

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

4

5 pts

Problem 1 Got It? Is the relation a function?

Yes

No

5

10 pts

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

6

10 pts

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

7

5 pts

Problem 1 Got It? Is the relation a function?

Yes

No

8

8

5 pts

Problem 2 Got It?

A

B

9

9

5 pts

Problem 2 Got It?

A

B

10

10

10 pts

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.

11

11

10 pts

Problem 4 Got It?

A

B

C

D

12

12

10 pts

Problem 5 Got It?

A

B

C

D

13

13

5 pts

Problem 5 Got It?

A

B

14

10 pts

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

Identify the domain of the relation.

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

{-2, -1, 0, 1}

{-3, 4, 5, 6}

15

10 pts

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

Identify the range of the relation.

{-2, -1, 0, 1}

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

{-3, 4, 5, 6}

16

10 pts

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.

17

17

5 pts

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

No, it is not a function.

Yes, it is a function.

18

10 pts

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

-2

3

9

43

19

10 pts

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}

20

5 pts

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

f(x) = 2x + 7

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

21

20 pts

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.

22

22

10 pts

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.

23

10 pts

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.

24

24

10 pts

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

25

30 pts

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

26

10 pts

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

27

10 pts

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

28

10 pts

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

29

10 pts

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.

30

100 pts

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.

31

10 pts

Reflection: Math Success

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