2. Linear Functions Day 1 (Module 17) Warm Up Pouring Peanuts Definition What is a Function? Guided Practices Is it a Functional Relationship? The “Functional” MP3 Definitions Function Notation Domain and Range Recap on Functions

3. The graph represents a real- world scenario. Examine the graph and answer the questions below. 1.What are the algebraic and real-world meanings of the point (0, 2000)? 2.What are the algebraic and real-world meanings of the point (500, 0)? 3.At what rate are the peanuts being poured? Pouring Peanuts (Warm Up) Y-intercept. At 0 sec. weight is 2000 oz. X-intercept. At 500 sec. weight is 0 oz. 4 oz. per sec.

4. Functions Create Frayer models for each of your definitions. They do not need to be big. Definitions Functions Domain Range Function Notation Relations There will be a vocabulary Check

5. What is a Function? (Definition) A FUNCTION is a relationship between input and output. In a FUNCTION, the output depends on the input. In a FUNCTION, there is exactly one output for each input. You can write a “depends on” sentence to help examine a FUNCTIONAL relationship. Your pay depends on the hours worked. dependent quantity y output independent quantity x is a function of input Glencoe Algebra I, Page 58

6. Is it a Functional Relationship? (Guided Practice) Examine each set of data below. Determine if it represents a functional relationship. Explain why or why not. 1 Grade you receive on a test and the number of problems missed 2 The amount of money you have and the amount of gas you put in your car 3 Your height and the width of your waist 4 Your height and your age The grade you receive on a test is a function of (depends on) the number of problems you missed. Therefore, this is a functional relationship. The amount of gas you put in your car is a function of (depends on) the amount of money you have. Therefore, this is a functional relationship. There is no relationship between your height and the width of your waist. Therefore, this is NOT a functional relationship. Your height is a function of (depends on) your age. Therefore, this is a functional relationship.

7. Apollo Process Column 1234512345 Rap Country Jazz Latin Classical What happens when I press 2? The “Functional” MP3 (Guided Practice) What happens when I press 4? Does this represent a function? If it represents a function, write a “depends on” sentence. If it represents a function, write a “function” sentence. A Country song will play A Latin song will play Yes The type of song played depends on the number selected. The type of song is a function of the number selected. 1 Dependent Output Independent Input

8. Apollo Process Column Dependent Output Independent Input 1234512345 Rap Country Jazz Latin Classical The “Functional” MP3 (Guided Practice) Remember that the definition stated that in a FUNCTION, there is exactly one output for each input. Let’s examine the table to determine if this is true. There is exactly one type of song (output) for each assigned number (input). 1

9. Apollo Process Column Dependent Output Independent Input 1234512345 Rap Country Jazz Latin Classical The “Functional” MP3 (Guided Practice) Rap Country Jazz Latin Classical 1234512345 1 Yes, this is a function. Does the table represent a function? Hint: Create a mapping.

10. Apollo 1234512345 Country Classical Rap Latin Rap Process Column Dependent y Independent x 2 The “Functional” MP3 (Guided Practice) Does the table represent a function? Yes, this is a function. 3154231542 Rap Country Latin Classical Hint: Create a mapping.

11. Apollo 3154231542 Rap Country Rap Latin Classical Process Column Dependent y Independent x 3 The “Functional” MP3 (Guided Practice) Does the table represent a function? 3154231542 Rap Country Latin Classical Yes, this is a function.

12. Apollo 3151231512 Rap Country Rap Latin Classical Process Column Dependent y Independent x 4 The “Functional” MP3 (Guided Practice) Does the table represent a function? 31523152 Rap Country Latin Classical No, this is NOT a function. If you press 1, which song would play?

13. Apollo 1234512345 Rap Process Column Dependent y Independent x 5 The “Functional” MP3 (Guided Practice) Does the table represent a function? 1234512345 Rap Yes, this is a function. There is exactly one output for each input.

14. Assignment Complete Apollo Chill assignment. Put it in your interactive notebook and get it checked by Mrs. Sims. Then start on the next slide

15. Function Notation (Definition) Equations that are functions can be written in a form called function notation. For example, instead of writing an equation as y = 3x – 8, you can replace the y with f (x). y = 3x – 8 f (x) So, how do we read “ f (x)”? Although it looks like we would read it as “f times x” or “f parentheses x”, we read it as Equation NotationFunction Notation “ f of x”. Read f (x) = 3x – 8 as “ f of x equals 3x minus 8”.

16. Function Notation (Definition) In a function, x represents the independent quantity, input, or the elements of the domain. f (x) represents y, the dependent quantity, output, or the elements of the range. For example, f (5), is the element in the range that corresponds to the element 5 in the domain. We say that f (5) is the function value of f for x = 5. Function Notation f (x) = 3x – 8 f (5) = 3(5) – 8 f (5) = 7 Glencoe Algebra I, Page 148

17. Function Notation (Definition) Not only can you use substitution to evaluate functions, you can examine the table and graph of the function. Substitution f (x)= –2x – 8 f (–1)= –2 (–1) – 8 f (–1)= –6 Table x f (x) –3–2 –4 –1–6 Graph f (x) = – 2x – 8 ( –1, – 6)

18. f (x) = {(2,0) (3,2) (5,6) (6,8)} 2 0 3 5656 2 6 8 f (5) = 6 2 0 3 5656 2 6868 Independent Dependent Domain Range xy x f(x) Function Notation (Definition) Let’s take a look at the function f(x) = 2x – 4 to further examine function notation as it connects to multiple representations. This function can be modeled by the relation {(2, 0), (3,2), (5,6), (6,8)}. Remember, a relation is simply a set of ordered pairs. Use the table feature of your calculator to verify the relation.

19. f (x) = {(1,15) (2,16) (3,17) (4,18) (5,19)} 1234512345 15 16 17 18 19 Domain Range Domain and Range (Definition) The set of the first numbers of the ordered pairs is the domain. The set of second numbers of the ordered pairs is the range. Does this relation and mapping represent a function? YES Explain. Each input value is assigned to exactly one output value.

20. f (x) = {(1,15) (2,16) (3,17) (4,18) (5,19)} Domain and Range (Definition) The domain and range can also be written as a relation. Domain = { 1, 2, 3, 4, 5} Range = { 15, 16, 17, 18, 19} Notice that the first elements in each ordered pair is part of the domain. The second elements in each ordered pair is part of the range.

21. Create A chart Create a chart that describes X and Y X Y

22. Recap on Functions (Definition) You have learned many ways to describe or represent the variables x and y. Fill in the chart below with those descriptors. xy Independent Quantity Dependent Quantity InputOutput DomainRange xf(x)

23. THE END