2. Identifying Relations and Functions A relation is a set of ordered pairs. The domain of the relation is x-coordinate of the ordered pair. It is also considered as the input (independent variable). The range of the relation is y-coordinate of the ordered pair. It is also considered as the output (dependent variable). Domain Range x1234 y57911 Input Output Another way to understand it is…

3. Understanding Functional Question: How do I buy some M&M’s without breaking the vending machine? Correct Answer: After I put my money in, I need to INPUT a value in order to get the M&M’s. But what’s missing? Correct Answer: The numbers! Let’s add some in. 12 34 56

4. Understanding Functional In order for something to be functional, you should know EXACTLY what given to you (the output) after you input your choice. Question: This is functional? 12 34 56 Input(Domain)Output(Range) 1granola bar 2pretzels 3popcorn 4chips 5M&M’s Yes, this is functional

5. Understanding Functional Let’s change the input around Question: This is functional? Do I know exactly what I will get after I input a choice? 12 3 6 Input(Domain)Output(Range) 1granola bar 2pretzels 3popcorn chips M&M’s No, this is not functional 4 5 3 3

6. Understanding Functional Again, let’s make changes Question: This is functional? Do I know exactly what I will get after I input a choice? 12 34 56 Input(Domain)Output(Range) 1granola bar 2 3popcorn M&M’s 4 5 6 Yes, this is functional

7. Is this a function? For a relation to be a function, one input (x) must have exactly one output (y). DomainRange 0 1 1 2 2 3 4 For example, is this a function? Explain. This is NOT a function; the input of 1 has two different outputs. DomainRange 0 1 1 2 2 3 4 This is a function; all inputs have exactly one output.

8. Examples DomainRange 0 1 1 3 2 2 4 Is this a function? Explain. This is a function, all inputs have exactly one output. A) (0,1), (1,3), (2,2), (3,4) 3 Mapping a diagram can be helpful DomainRange -2 3 2 2 This is NOT a function; the input of 2 has two different outputs. B) (-2,3), (2,2), (2,-2)

9. Graphing Relations and Functions Let’s graph Example B to see how it looks. Remember, this graph shows something NOT functional. B) (-2,3), (2,2), (2,-2) x y 1234 Let’s see another graph NOT functional. x y 1234 Question: Why is this NOT functional?

10. Graphing Relations and Functions Vertical Line Test x y 1234 x y 1234 If you can find a vertical line that passes through two points on the graph, then the relation is NOT a function. Use your pencil as a vertical line, and check. Oh no!!! TWO points! TWO points! Failed!

11. Function Rule Describes the operation performed on the domain to get the range. When written as an equation it is a function notation.

12. Function Notation f(x) Equation y= 2x +3 Solve for y if x=4 Y=2(4) +3 Y=8+3 Y=11 Function Notation

13. f(x)=6x+5, find each function value a. f(7) f(7) = 6(7) +5 f(7)=42 +5 f(7)=47 b. f(-4) f(-4) = 6(-4) +5 f(-4) = -24 +5 f(-4)= -19

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