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

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

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

The charges for a short-term car park:

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

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.

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

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.

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?

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.

Is this Graph a Function?

Let’s see how you did….

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

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

INPUT OUTPUT FUNCTION MACHINE domain range

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

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

3) Identify the domain and range:

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