Functions
Download as PPT, PDF0 likes415 views
1. The document defines analytic plane quadrants and ordered pairs. 2. An ordered pair (a,b) contains two elements where a is the first component and b is the second. Equality of ordered pairs means the first elements are equal and the second elements are equal. 3. Notations for intervals are defined including closed, open, and half-open intervals using brackets [], parentheses (), and brackets with parentheses [).
![Notations of intervals: Let a and b be real numbers. A = [a, b] denotes the set of all real numbers between a and b (a and b are included). a b](https://image.slidesharecdn.com/functions-120114005335-phpapp02/85/Functions-7-320.jpg)
![a b A = (a, b] denotes the set of all real numbers between a and b (a is excluded and b is included).](https://image.slidesharecdn.com/functions-120114005335-phpapp02/85/Functions-9-320.jpg)
Functions
- 1. Functions
- 2. Analytic plane x-axis y-axis origin 1 st quadrant (+,+) 2 nd quadrant (-,+) 3 rd quadrant (-,-) 4 th quadrant (+,-)
- 3. Ordered Pair: Given that a and b are any two elements, (a,b) is called an ordered pair where a is first component and b is second component.
- 4. Example: ( 5 , -1) ( abu , elham) ( a , b) ( square , triangle) ( adhaser , 165 cm) ( emanuel , ?)
- 5. Example: y = x – 2. Give four example for the ordered pair (x, y).
- 6. Equality of ordered pairs Let (m, n) and (p, q) be two ordered pairs. (m, n) = (p, q) if and only if m = p and n = q. Example: find x and y if (x + 1, 6) = (8, 2y – 4)
- 7. Notations of intervals: Let a and b be real numbers. A = [a, b] denotes the set of all real numbers between a and b (a and b are included). a b
- 8. a b A = (a, b) denotes the set of all real numbers between a and b (a and b are excluded). A = [a, b) denotes the set of all real numbers between a and b (a is included and b is excluded). a b
- 9. a b A = (a, b] denotes the set of all real numbers between a and b (a is excluded and b is included).