1. What is a Function Teacher Notes
Notes: Today students will create their understanding of a function: “In a function each input has only one output”. We will not use independent and dependent variables.
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2. 2-7 Solving Equations With Algebra Tiles powerpoint
Practice Target
Practice 6: Attend to precision. [Students] try to use clear definitions in discussion with others and in their own reasoning.
Practice 4: Model with mathematics.
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3. Do you know what a function is?
2-7 Solving Equations With Algebra Tiles powerpoint
Learning Target
Connecting Patterns & Functions Target
F-IFa I can understand the concept of a function and
use function notation.
F‐IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Do you know what a function is?
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4. What does the word “function” mean.
Launch
What does the word “function” mean.
Can you define it?
Can you use it in a sentence?
Can you give an example?
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5. Explore
Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License

6. Today we will learn the definition of a function in algebra.
Use the following examples to
develop your own definition of
the word function in algebra.
Do not give them the definition of function. Have them develop the meaning through comparing tables, then graphs and then situations that are and are not functions.
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7. What do you notice? What do you think a function is?
This table is not a function.
This table is a function.
Input
Output 1 3 2 5 7 4 9 11
Input
Output 1 10 2 3 7 4 5 12
DO NOT DISUCSS AS A CLASS YET.
Just let them wrestle with it.
FYI: Not a function since the input 1 has two outputs 10 and 12.
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8. What do you notice? What do you think a function is?
This table is a function.
This table is not a function.
Input
Output 4 7 9 2 1 10 5 13
Input
Output 9 10 4 3 8 7 2 5 15
DO NOT DISUCSS AS A CLASS YET.
Just let them wrestle with it.
FYI: Not a function since the input 4 has two outputs 3 and 12.
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9. What do you notice? What do you think a function is?
This table is a function.
This table is not a function.
Input
Output 7 5 14 -4 -9
Input
Output 5 7 14 -4 -9
DO NOT DISUCSS AS A CLASS YET.
Just let them wrestle with it.
FYI: Not a function since the input 5 has outputs 7, 5, 14, -4 and -9.
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10. What do you think a function is?
Have the class come up with a working definition of a function. Do not give them a definition. We will continue to refine the definition through this presentation.
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11. Is this table of the L(x) pattern a function? Defend your answer.
Input
Output 1 3 2 5 7 4 9 11
Yes since each input has only 1 output.
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12. Is this table a function? Defend your answer.
Input
Output 7 -1 2 4 -3 -7 9 11 -5
NO. Input -3 has outputs -7 and -5.
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13. What do you notice? What do you think a function is?
This graph is a function.
This graph is not a function.
There is a 10 second timer on this slide.
The next slide tells students to connect the graph to what they know about tables.
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14. Advance to see the last slide repeated.
How can you use what you know about tables to help you determine if a graph is a function?
Advance to see the last slide repeated.
Advance to see the last slide repeated.
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15. What do you notice? What do you think a function is?
This graph is a function.
This graph is not a function.
There is a 10 second timer on this slide.
The next slide tells students to connect the graph to what they know about tables.
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16. This graph is a function. This graph is not a function.
What do you notice? What do you think a function is?
This graph is a function.
This graph is not a function.
Not a function since the all inputs except x = 0 have two outputs.
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17. What do you think a function is?
Have the class come up with a working definition of a function. Do not give them a definition. We will continue to refine the definition through this presentation.
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18. Is this graph a function? Defend your answer.
This is not a function since x = -1 has two outputs, 3 and -3.
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19. Is this graph a function? Defend your answer.
This is a function.
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20. Here is a way to test if a graph is a function.
The graph is
a function
The Vertical Line Test. Pass a vertical line over the graph. If the vertical line touches the graph only once, then the graph is a function.
Now we show the vertical line test, but we still want students to develop their own understanding.
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21. Here is a way to test if a graph is a function.
The graph is not a function
The Vertical Line Test. Pass a vertical line over the graph. If the vertical line touches the graph more than once, then the graph is not a function. x x
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22. Why does the Vertical Line Test work?
Use what you know about functions and tables to help you answer this question.
Help them to make the connection between the table and the graph.
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23. What do you think a function is?
It’s the same for a table and a graph.
Have the class come up with a working definition of a function. Do not give them a definition. We will continue to refine the definition through this presentation.
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24. Is this graph a function?
This is a function.
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25. Is this graph a function? Defend your answer.
This is a function.
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26. Is this graph a function? Defend your answer.
This is not a function < x < has three outputs.
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27. Is this situation a function? Defend your answer.
The year a person was born and the first year they can get a driver’s license.
This is a function. Rule: birth year + 16 = driver’s license year.
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28. Is this situation a function? Defend your answer.
The forecasted high temperature of a day and the low temperature of the same day.
This is not a function.
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29. Debrief
Quick Write…
Describe your way of deciding if a graph, table or situation is a function.
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30. Rate your understanding of the target from 1 to 5.
2-7 Solving Equations With Algebra Tiles powerpoint
Learning Target 5 3 1 2 4
Did you hit the targets?
I can understand the concept
of a function & use function notation.
I can determine whether a table, equation, ordered pairs or a situation is a function.
Rate your understanding of the target from 1 to 5.
Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License