Algebra 1 4-3 Patterns and Nonlinear Functions

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by Matthew Richardson

| 35 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.

Solve It! The table below shows the relationship between the number of steps in the staircase below and the number of blocks needed to build the staircase.

1

2

3

4

1

10 pts

Solve It! How many blocks are required to build 4 steps? Enter only a number.

2

1 pt

Solve It! What is the ordered pair associated with 4 steps?

(4, 10)

(4, 15)

(4, 13)

(4, 6)

3

1 pt

Solve It! How many blocks are required to build 5 steps? Enter only a number.

4

1 pt

Solve It! What is the ordered pair associated with 5 steps?

(4, 15)

(5, 19)

(5, 15)

(4, 10)

5

10 pts

Problem 1 Got It? The table shows the fraction A of the original area of a piece of paper that remains after the paper has been cut in half n times. Graph the function represented by the table.

6

6

10 pts

Problem 1 Got It? Is the function represented by the table and graphed in the previous item linear or nonlinear?

Enter a one-word response.

7

7

10 pts

Problem 1 Got It? Reasoning: Will the area, A, ever reach zero? Explain.

8

9

10

11

12

8

5 pts

Problem 2 Got It? Enter a number to fill the table.

9

5 pts

Problem 2 Got It? Enter a number to fill the table.

10

10 pts

Problem 2 Got It? Represent the relationship using words.

11

10 pts

Problem 2 Got It? Represent the relationship using an equation.

A

B

C

D

12

10 pts

Problem 2 Got It? Represent the relationship using a graph.

NOTE: Not all points from the table must be on your graph.

Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

13

13

10 pts

Problem 3 Got It?

A

B

C

D

14

10 pts

Graph the function represented by the table.

15

5 pts

Is the function you graphed in the item above linear or nonlinear?

Nonlinear

Linear

16

10 pts

This set of ordered pairs represent a function.

What is a rule that represents this function?

y = 2x + 2

y = x - 2

y = 3x - 2

y = 2x - 3

17

17

10 pts

Which rule could represent the function shown by the table?

A

B

C

18

19

18

5 pts

Vocabulary: Does the graph represent a linear function or a nonlinear function?

Linear function

Nonlinear function

19

10 pts

Explain.

20

21

20

5 pts

Vocabulary: Does the graph represent a linear function or a nonlinear function?

Linear function

Nonlinear function

21

10 pts

Explain.

22

22

10 pts

Error Analysis: A classmate says that the function shown by the table can be represented by the rule y = x + 1. Describe and correct your classmate's error. Use ^2 notation for exponents, if necessary.

23

10 pts

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

18

-18

-24

-76

24

10 pts

Review Lesson 1-2: Evaluate the expression for x = 0.

Enter only a number.

25

10 pts

Review Lesson 1-2: Evaluate the expression for x = 2.5.

Enter only a number.

26

10 pts

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

Enter only a number.

27

10 pts

Review Lesson 1-2: Evaluate the expression for x = 0.

Enter only a number.

28

10 pts

Review Lesson 1-2: Evaluate the expression for x = 2.5.

Enter only a number.

29

10 pts

Vocabulary Review: Find the next number in the pattern.

Enter only a number.

30

10 pts

Vocabulary Review: Find the next number in the pattern.

Enter only a number.

31

10 pts

Vocabulary Review: Find the next number in the pattern.

Enter only a number.

32

10 pts

Vocabulary Review: Find the next number in the pattern.

Enter only a number, in this format: 1/9.

33

33

10 pts

Vocabulary Review: The next shape in the pattern below has __?__ blocks.

Enter only a number to fill in the blank.

34

34

10 pts

Use Your Vocabulary: Identify the graphs that represent a nonlinear function.

Select all that apply.

A

B

C

D

35

10 pts

Reflection: Math Success

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