Functions
Download as PPT, PDF1 like230 views
1. The document defines analytic plane quadrants and ordered pairs. 2. An ordered pair (a,b) has a as the first element and b as the second element. Equality of ordered pairs means that the first elements are equal and the second elements are equal. 3. The document also defines notations for intervals on the real number line including closed, open, and half-open intervals.
![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-110726084731-phpapp01/85/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-110726084731-phpapp01/85/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).