Functions

Lesson 2

Math

Unit 4

8th Grade

Lesson 2 of 12

Objective


Use function language to describe functions. Identify function rules.

Common Core Standards


Core Standards

  • 8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.

Criteria for Success


  1. Analyze a function table to find a rule that takes the input values and produces the output values. 
  2. Use function language to describe one set as a function of another set; for example, $$y$$ is a function of $$x$$ because for every $$x $$ input, there is exactly one $$y$$ output. 
  3. Complete input/output tables based on function rules. 

Tips for Teachers


In this lesson, focus on students using appropriate and correct language when describing functions and non-functions. They should use terminology including “input”, “output”, “function of”, etc. and use the context of the situation to help them make sense of the situation (as in Anchor Problem #2). Use small group or partner work where appropriate to ensure all students have the opportunity to describe functions and use function language. 

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Anchor Problems


Problem 1

A function machine takes an input and, based on some rule, produces an output.

The tables below show some input-output pairs for different functions. For each table, describe a function rule in words that would produce the given outputs from the corresponding inputs. Then fill in the rest of the table values as inputs and outputs that are consistent with that rule.
 

a.   Input values can be any English word. Output values are letters from the English alphabet.

Input cat house you stem      
Output t e u   z    

b.   Input values can be any rational number. Output values can be any rational number.

Input 2 5 -1.53 0 -4    
Output 7 10 3.47 5   8  

Guiding Questions

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References

Illustrative Mathematics Function RulesParts a and b

Function Rules, accessed on Oct. 26, 2017, 8:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

The table below shows the total distance a runner has covered over a given period of time. 

Time in minutes (t) 1 2 3 4 5 6 7 8 9 10
Total distance in miles (d) 0.1 0.25 0.35 0.43 0.5 0.5 0.5 0.62 0.71 0.85

a.   Is distance, $$d$$, a function of time, $$t$$? Explain.

b.   Is time, $$t$$, a function of distance, $$d$$? Explain. 

Guiding Questions

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Problem 3

Two input/output tables are shown below. 

Table A:

Input Output
3 –5
2 –4
1 –3
2 –2
3 –1

Table B:

Input Output
–8 14
–2  
1 6
  0
9 –2

a.   Table A is not a function. Change the table so that it is a function. 

b.   Table B is not a function. Complete the table with values to show it is not a function.

Guiding Questions

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Problem Set

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Target Task


At a local bank, when you open an account, you provide certain information that is stored in the bank's records. The table below shows the names and mailing zip codes of some of the bank's customers. 

Customer Name Zip Code
Tyler Jackson 70114
Justine Goodman 12084
Tristan Manuel 30311
Vanera Caro 30311
Mia Lee 20815

a.   Suppose F is the rule that takes a customer's name and provides their mailing zip code. According to the information in this table, is F a function? Explain your reasoning. 

b.   Suppose G is the rule that takes a customer's mailing zip code and provides their name. According to the information in this table, is G a function? Explain your reasoning. 

c.   If the bank is looking for a way to identify specific customers, why would using their zip code not be a good way to do this? What other input might the bank use instead?

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 1

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Lesson 3

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Defining Functions

Topic B: Representing and Interpreting Functions

Topic C: Comparing Functions

Topic D: Describing and Drawing Graphs of Functions

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