1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

2. Objective 1. To identify a function from a relation. 2. To identify the domain and range of a function. 3. To evaluate a function written in function notation. Sections 9A – Relations and Functions

3. The charges for a short-term car park Turn to page 268

4. The charges for a short-term car park:

5. The charges for a short-term car park Relation: In mathematical terms, a relationship between two variables (i.e. time and cost).

6. A relation… Can be represented by a finite number of ordered pairs. – {( 1, 5), (-2, 3), (4, 3), (1, 6)} Or an infinite number of ordered pairs. – {0 <t<24} any real infinite number of t time for parking costs.

7. A relation… Can be a graph. Can be an equation. y = x +3

8. INPUT OUTPUT FUNCTION MACHINE one input must have one and only one output. Function: is a special kind of relation where no two ordered pairs have the same x-coordinate.

9. 1) {(2,5), (3,8), (4,6), (7, 20)} 2) {(1,4), (1,5), (2,3), (9, 28)} 3) {(1,0), (4,0), (9,0), (21, 0)} Is this a function?

10. Vertical Line Test Is a way to determine if a relation is a function. If a vertical line can cross a curve in more than one place at the same time,then it is NOT a function. Demo in your e-text on page 270.

11. Is this Graph a Function?

20. Let’s see how you did….

21. Answers: 1. YES 6. NO 2. YES 7. YES 3. NO 8. YES 4. NO 9. NO 5. YES 10. YES

22. Section 9B – Domain and Range Domain: – is the set of possible x-values. Range: – is the set of possible y-values.

23. INPUT OUTPUT FUNCTION MACHINE domain range

24. 1) Identify the domain and range: The domain is: The range is:

25. 2) Identify the domain and range: The domain is: The range is:

26. 3) Identify the domain and range:

27. Homework Exercise 9A, pg 270 – #1ace, #2all Exercise 9B, pg 273 – #1bdfhi, #2aceg