1. Objectives: To determine whether a relation is a function To find domain and range and use function notation Formalizing Relations and Functions

2. Relation: a pairing of numbers in one set with numbers in another setDomain: the set of x-valuesRange: the set of y-values

3. Problem #1: Identifying Functions Using Mapping Diagram Identify the domain and range of the relation. Represent the relation with a mapping diagram. Is the relation a function? A) A){(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}

4. Problem #1: Identifying Functions Using Mapping Diagram Identify the domain and range of the relation. Represent the relation with a mapping diagram. Is the relation a function? B) B){(6,5), (4,3), (6,4), (5,8)}

5. Problem #1 Got It? Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation a function?

6. Another method used to determine if a relation is a function. Look at the graph and determine if any vertical line passes through more than one point of the graph, then the relation is not a function.

7. Problem #2: Identifying Functions Using the Vertical Line Test Is the relation a function? Use the Vertical Line Test. A) A) {(-4, 2), (-3, 1), (0,-2), (-4, -1), (1, 2)}

8. Problem #2: Identifying Functions Using the Vertical Line Test Is the relation a function? Use the Vertical Line Test.

9. Problem #2 Got It? Is the relation a function? Use the Vertical Line Test.

11. Problem #3: Evaluating a Function A) The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 8 minutes?

12. Problem #3: Evaluating a Function

13. Problem #3 Got It? The function T(x) = 65x represents the number of words T(x) that Rachel can type in x minutes. How many words can she type in 7 minutes?

14. Textbook Page 271; #1 – 3, 5 – 17 All

16. Objectives: To determine whether a relation is a function To find domain and range and use function notation Continued…

17. Problem #4: Finding the Range of a Function A) Multiple Choice The domain of f(x) = 1.5x + 4 is {1, 2, 3, 4}. What is the range?

18. Problem #4: Finding the Range of a Function B) The domain of g(x) = 4x – 12 is {1, 3, 5, 7}. What is the range?

19. Problem #4 Got It? What is the range of f(x) = 3x – 2 with domain {1, 2, 3, 4}?

20. Problem #5: Identifying a Reasonable Domain and Range

22. B) Lorena has 4 rolls of ribbon to make party favors. Each roll can be used to make 30 favors. The function F(r) = 30r represents the number of favors F(r) that can be made with r rolls. What are a reasonable domain and range of the function? What is a graph of the function?

24. Problem #5 Got It? A car can travel 32 miles for each gallon of gasoline. The function d(x) = 32x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. The car’s fuel tank holds 17 gal. Find a reasonable domain and range for each function. Then graph the function.

26. 4 – 6 Worksheet