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