Recognize Relation-Function Part 1 edmodo
- 1. POD 1. What is the longest distance between any two points in a crate with the following dimension: Length 10 feet Width 9 feet Height 4 feet
- 2. Functions Unit 4 Part 1 CC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
- 3. What is a Relation? A rule that gives an output number for every valid input number A set of ordered pairs for which all x and y values are related in the same way. No special rules need apply. The following are examples of relations: {(1,2), (1, 4), (1, 5), (1, 6), (1, -3)} {(1,2), (2, 4), (3, 5), (2, 6), (1, -3)}
- 4. What is a Function? A rule of matching elements of two sets of numbers in which an input value from the first set has only one output value in the second set. Every value of x has a unique value of y. function: {(1,2), (2, 4), (3, 5), (4, 6), (5,-3)}
- 5. What Will You Get? If you combine cake mix, eggs and milk and put it in the oven, what will come out? Cake mix
- 6. What Will You Get If you combine the ingredients again and put it in the oven, what will come out? Cake mix
- 7. Domain • In a function, the possible values for x in the given situation. • It is the set of values of the independent variable of a given function. function: {(1,2), (2, 4), (3, 5), (4, 6), (5,-3)} Domain: {1, 2, 3, 4, 5}
- 8. Range • In a function, the possible values for y in the given situation. • It is the set of values of the dependent variable of a given function. function: {(1,2), (2, 4), (3, 5), (4, 6), (5,-3)} Range: {2, 4, 5, 6, -3}
- 9. Relations and Functions • Relations and functions can also be represented as relationships between two sets of elements Input Output Input Output x-values y-values x-values y-values Domain Range Domain Range 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 Relation/Function Relation/Not a Function
- 10. Relations and Functions • Now you try. Determine whether each set is a relation, a function, or both. 3 5 Amy Bob 6 10 Liz Joe 9 15 Sara Dan 21 a b 2 2 e c 4 4 i d 6 6 o f 8 8
- 11. Relations and Functions • We will look at functions in four different ways 1. Numerically; tables and ordered pairs 2. Graphically 3. Verbally 4. Algebraically
- 12. Functions-- Numerically • For each x value, you can have one, and only one, y value • Check each table for repeating x’s x y x y 4 2 4 4 2 2 2 2 0 0 0 0 -2 -2 2 -2 -4 -4 4 -2
- 13. Functions-- Numerically • For each x value, you can have one, and only one, y value • Check each set of ordered pairs for repeating x’s • {(4,4), (2,2), (0,0), (-2,-2), (-4,-4)} • {(4,4), (2,2), (0,0), (2,-2), (4,-4)}
- 14. Functions-- Graphically • For each x value, you can have one, and only one, y value • Check that each x-coordinate is related to only one y-coordinate
- 15. Functions--Graphically • For each x value, you can have one, and only one, y value • Check that each x-coordinate is related to only one y-coordinate
- 16. Functions--Verbally • It is a surprising biological fact that most crickets chirp at a rate that increases as the temperature increases. For the snowy tree cricket (Oecanthus fultoni), the relationship between temperature and chirp rate is so reliable that this type of cricket is called the thermometer cricket. We can estimate the temperature (in degrees Fahrenheit) by counting the number of times a snowy tree cricket chirps in 15 seconds and adding 40. For instance, if we count 20 chirps in 15 seconds, then a good estimate of the temperature is 20 + 40 = 60 F◦
- 18. Functions--Algebraically • For each x value, you can have one, and only one, y value • Check that each x-value in your domain relates to only one y-value in your range. x y=x+1 y -2 -2 + 1 -1 y=x+1 -1 -1 + 1 0 0 0+1 1 1 1+1 2 2 2+1 3 3 3+1 4
- 19. Functions
Editor's Notes
- #4: Discuss ordered pairs, x values and y values.x is the input or independent variabley is the output or dependent variablePoint out the relationship between the x and y values in each ordered pair.
- #5: Again point out the relationship in each ordered pair, but this time show that each x value has a unique y value.
- #6: If you mix the ingredients and put it in the oven, only a cake can come out.
- #7: If you mix the ingredients again can you get a turkey out? Can you get a basketball out? No, you will always get a cake out.In a function, if you put the same thing in, you will always get the same thing out—for every input (x) value there is only one output (y) value.
- #8: Point out the inputs (x values) in the set.
- #9: Point out the Outputs (y values) in the set.
- #10: Show different representation of a relation/function.
- #11: Point out that relations/functions can be sets of any kind of elements , not just numbers
- #15: Point out that in the absolute value function when x is 1, y is 1 and nothing else; and when x is -1, y is 1 and nothing else.Emphasize that each x (input) value relates to only one y (output) value.
- #16: Point out x coordinates that relate to more than one y coordinate. Emphasize that if any x coordinate has more than one y coordinate the relation is NOT a function.
- #18: Point out that you wouldn’t say “I have 5 gallons of paint, how much wall can I paint?” Instead, you would say “the walls in my room have 400 square feet, how much paint will I need?”