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# Functions

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### Functions

1. 1. Functions
2. 2. Analytic plane x-axis y-axis origin 1 st quadrant (+,+) 2 nd quadrant (-,+) 3 rd quadrant (-,-) 4 th quadrant (+,-)
3. 3. Ordered Pair: <ul><li>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. </li></ul>
4. 4. Example: <ul><li>( 5 , -1) </li></ul><ul><li>( abu , elham) </li></ul><ul><li>( a , b) </li></ul><ul><li>( square , triangle) </li></ul><ul><li>( adhaser , 165 cm) </li></ul><ul><li>( emanuel , ?) </li></ul>
5. 5. Example: <ul><li>y = x – 2. Give four example for the ordered pair (x, y). </li></ul>
6. 6. Equality of ordered pairs <ul><li>Let (m, n) and (p, q) be two ordered pairs. </li></ul><ul><li>(m, n) = (p, q) if and only if m = p and n = q. </li></ul><ul><li>Example: find x and y if (x + 1, 6) = (8, 2y – 4) </li></ul>
7. 7. Notations of intervals: <ul><li>Let a and b be real numbers. </li></ul>A = [a, b] denotes the set of all real numbers between a and b (a and b are included). a b
8. 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. 9. a b A = (a, b] denotes the set of all real numbers between a and b (a is excluded and b is included).