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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License.  2014-2015 Page 1 of 1 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 2

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? Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

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? Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

Explore Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 6

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 7

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 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 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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 9

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 10

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 11

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 12

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 13

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 14

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 15

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 16

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 17

Is this graph a function? Defend your answer. This is not a function since x = -1 has two outputs, 3 and -3. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 18

Is this graph a function? Defend your answer. This is a function. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 19

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 20

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 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 22

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 23

Is this graph a function? This is a function. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 24

Is this graph a function? Defend your answer. This is a function. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 25

Is this graph a function? Defend your answer. This is not a function -2.5 < x < 2.5 2 has three outputs. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 26

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 27

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. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015 28

Debrief Quick Write… Describe your way of deciding if a graph, table or situation is a function. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 2014-2015

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. 2014-2015