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Session 5, Part D:
Putting It Together (35 minutes)

Linear functions have come up in many situations so far in this session. In this section, we'll consolidate some of our ideas about linear functions and look for connections between them. Note 14

Below are several input/output tables. For each table:
Note 15

• 

Find a closed form rule for taking an input and finding the correct output

• 

Find a recursive rule for going from one output to the next

• 

Graph the pairs of numbers in the table

• 

Determine if the rule describes a linear function or not. If it is a linear function, find the slope.

Problem D1

Solution  

Input

 

Output

1

 

0

2

 

1

3

 

2

4

 

3

5

 

4

 

 

Problem D2

Solution  

Input

 

Output

1

 

1

2

 

4

3

 

9

4

 

16

5

 

25

 

Stop! Do the above problem before you proceed. Use the tip text to help you solve the problem if you get stuck.
The recursive rule here includes n, the input number.   Close Tip

 

Problem D3

Solution  

Input

 

Output

1

 

3

2

 

5

3

 

7

4

 

9

5

 

11

 

 

Problem D4

Solution  

Input

 

Output

1

 

9

2

 

8

3

 

7

4

 

6

5

 

5

 

 

Problem D5

Solution  

Input

 

Output

1

 

5

2

 

10

3

 

15

4

 

20

5

 

25

 

 

Problem D6

Solution  

Input

 

Output

1

 

1

2

 

1/2

3

 

1/3

4

 

1/4

5

 

1/5

 

 

Problem D7

Solution  

Input

 

Output

1

 

-7

2

 

-7

3

 

-7

4

 

-7

5

 

-7

 

 

Problem D8

write Reflect  

What are the characteristics of a linear function? How can you tell that a function is linear if you are given:

• 

a closed form rule for a function?

• 

a recursive rule for a function?

• 

a description of a situation?

• 

a table?

• 

a graph?

Next > Part E: Thinking About Technology

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