1) A function is a relationship between two sets of data where each input value in the domain corresponds to exactly one output value in the range. 2) Function notation represents a relationship as f(x) where x is plugged into the original equation. For example, the function f(x)=5x+9 defines the relationship. 3) To determine if a graph represents a function, the vertical line test can be used. If a vertical line can only intersect the graph in one point, it passes the test and is a function. If a line intersects in multiple points, it is not a function.

1. FunctionsBy: Samantha AdamsTechnology in Education

2. Key ConceptsWhat is a function?What is function notation?How to recognize functions by graphsLet’s start with a example

3. Example #1At the beginning of the year each student is assigned a teacher. Johnny Mrs. MorganSally Mrs. BrownJane Mr. BlackMichael Mr. WhiteDoug Mrs. JonesSo for each student there is one teacher.This represents a function.

4. What is a function…A relationship between two or more sets of data so that:The x-variable (domain) corresponds to only ONE y-variable (range)Let’s look at an example with numbers

5. Example #2Tell whether or not these are functions..{ (0,1), (3,6), (4,3), (1,8) }b. { (9,3), (4,8), (1,9), (3,5) }{ (9,4), (9,6), (9,1), (9,2) }

6. Example #2 ExplanationFirst list the domain and range for eachA. 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}Notice that in A. and B. each x corresponds to one yTherefore it is a functionIn C. one x corresponds to four (4) yTherefore it is not a function

7. What is function notation?An equation y= 2x+5 To be function notation change the y to f(x)Therefore f(x)= 2x+5In f(x) the x is what is plugged in for x in the equationLet’s take a look at an example

8. Example #3Solve f(x)= 5x+9X= -2

9. X= -1

10. X= 0

11. X= 1

12. X= 2Remember plug the numbers in for x

13. Take X= -2, 2Solve f(x)= 5x+9 X= -2 F(-2)= 5(-2)+9 F(-2)= -10+9 F(-2)= -1Solve f(x)= 5x+9 X= 2 F(2)= 5(2)+9 F(2)= 10+9 F(2)= 19