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# Functions

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### Functions

1. 1. Functions<br />By: Samantha AdamsTechnology in Education <br />
2. 2. Key Concepts<br />What is a function?<br />What is function notation?<br />How to recognize functions by graphs<br />Let’s start with a example<br />
3. 3. Example #1<br />At the beginning of the year each student is assigned a teacher. <br />Johnny Mrs. Morgan<br />Sally Mrs. Brown<br />Jane Mr. Black<br />Michael Mr. White<br />Doug Mrs. Jones<br />So for each student there is one teacher.<br />This represents a function.<br />
4. 4. What is a function…<br />A relationship between two or more sets of data so that:<br />The x-variable (domain) corresponds to only ONE y-variable (range)<br />Let’s look at an example with numbers<br />
5. 5. Example #2<br />Tell whether or not these are functions..<br />{ (0,1), (3,6), (4,3), (1,8) }<br />b. { (9,3), (4,8), (1,9), (3,5) }<br />{ (9,4), (9,6), (9,1), (9,2) }<br />
6. 6. Example #2 Explanation<br /><ul><li>First list the domain and range for each</li></ul>A. domain {0,3,4,1} range {1,6,3,8}B. domain {9,4,1,3} range {3,8,9,5}C. domain {9,9,9,9} range {4,6,1,2}<br />Notice that in A. and B. each x corresponds to one y<br />Therefore it is a function<br />In C. one x corresponds to four (4) y<br />Therefore it is not a function<br />
7. 7. What is function notation?<br />An equation y= 2x+5 <br />To be function notation change the y to f(x)<br />Therefore f(x)= 2x+5<br />In f(x) the x is what is plugged in for x in the equation<br />Let’s take a look at an example<br />
8. 8. Example #3<br />Solve f(x)= 5x+9<br /><ul><li>X= -2
9. 9. X= -1
10. 10. X= 0
11. 11. X= 1
12. 12. X= 2</li></ul>Remember plug the numbers in for x<br />
13. 13. Take X= -2, 2<br />Solve f(x)= 5x+9<br /> X= -2 <br /> F(-2)= 5(-2)+9 <br /> F(-2)= -10+9<br /> F(-2)= -1<br />Solve f(x)= 5x+9<br /> X= 2 <br /> F(2)= 5(2)+9 <br /> F(2)= 10+9<br /> F(2)= 19<br />
14. 14. Graphs of Functions<br />Graph 1<br />Graph 2<br />Graph 3<br />In order to tell if the graph is a function it must pass the vertical line test (VLT).<br /> - VLT is done by drawing a vertical line through any point of the graph and it only cuts the line once.<br />
15. 15. Graph of Functions Cont&apos;d<br />Graph 3<br />Graph 2<br />Graph 1<br />The first and third graphs are both examples of functions<br />The dashed line cuts the graph once<br />The middle graph is not a function<br />The dashed line passes through three (3) times<br />
16. 16. Overview<br />A function is a relation between x (domain) and y (range).<br />Where each x corresponds to one y<br />How to put an equation in function notation<br />Change y to f(x) <br />Lastly how to recognize if a graph is that of a function<br />It has to pass the vertical line test<br />
17. 17. END<br />