2­1 Relations and Functions 2010 September 10, 2010 {(2,0), (4,1), ( 3,­5)} y= (3 x+ 2) /( 4x ­1) 2.1 Relations & Functions Objective: Graph relations & identify functions. Th e num the am ber of wid ge ount o f cons ts produce d tructio n mate at a widge t f rial av ailable actory is pa . If the rt re are ly depende 4.2 m n illion . t on .. 3 5 5 0 ­1 5 Sep 16 ­ 12:40 PM 1 2­1 Relations and Functions 2010 September 10, 2010 Check Skills You'll Need Graph each ordered pair on the coordinate plane. 1. A (­4, ­8) 2. B (3, 6) 3. C (0, 0) 4. D (­1, 3) 5. E (­6, 5) Evaluate each expression for x = ­1, 0, 2, and 5 2 6. 2x + 1 7. | x ­ 3 | Sep 16 ­ 12:47 PM 2 2­1 Relations and Functions 2010 September 10, 2010 h c a e h ic h h w t i n i w d n e o i r i t a a . l . p . e r e s i g a n n i s a i a r on e dom in the i t c n h t t u n f f e o A t m n e l e e elem tly one c exa Sep 16 ­ 12:47 PM 3 2­1 Relations and Functions 2010 September 10, 2010 Are the following examples of functions? 1 2 Dec The price of a ski lift ticket is Jan related to which month you wish Feb Mar to ski. Apr y = 3x 2 $37 $42 $50 $50 $44 -4 squips 3 4 borks A b 1 2 3 4 A B C Teacher explanation: While this IS a function, it is not a one­to­one function. In a one­ to­one function, each member of the range "comes from" only one member of the domain. Sep 16 ­ 12:44 PM 4 2­1 Relations and Functions 2010 September 10, 2010 Vertical Line Test If a vertical line passes through at least two points on the graph, then one element of the domain is paired with more than one element of the range. Therefore the relation is not a function. Examples: Sep 16 ­ 12:47 PM 5 2­1 Relations and Functions 2010 September 10, 2010 A function rule expresses an output value in terms of an input value. Examples of function rules input y = 2x output input input f(x) = x + 5 output C = d output Sep 16 ­ 12:47 PM 6 2­1 Relations and Functions 2010 September 10, 2010 Reading function notation y = 3x + 2 f(x) = 3x + 2 3 facts: f(x) is pronounced "f of x" "a function f of x" f(x) does not mean "f times x" Sep 16 ­ 12:47 PM 7 2­1 Relations and Functions 2010 Input Function September 10, 2010 Output Ordered pair 5 Subtract 1 4 (4, 5) a Add 2 a + 2 (a, a + 2) 3 g g(3) (3, g(3)) x f f(x) (x, f(x)) Sep 16 ­ 12:47 PM 8 2­1 Relations and Functions 2010 September 10, 2010 Sep 10­10:25 AM 9 2­1 Relations and Functions 2010 September 10, 2010 real world connection The area of a square tile is a function of the length of a side of the square. Write a function rule for the area of a square. 2 Relate: area of a square is (side length) Define: Let s = the length of one side of the square tile. Then A(s) = the area of the square tile Write: A(s) = s 2 Sep 9 ­ 12:17 PM 10 2­1 Relations and Functions 2010 September 10, 2010 Sep 10­10:31 AM 11 2­1 Relations and Functions 2010 September 10, 2010 real world connection The area of a square tile is a function of the length of a side of the square. Write a function rule for the area of a square. Evaluate the function for a square with side length 3.5 in. A(s) = s 2 2 A(3.5) = (3.5) = 12.25 Substitute 3.5 for s. Simplify. Sep 9 ­ 12:17 PM 12 2­1 Relations and Functions 2010 September 10, 2010 Evaluating Functions Given the function: a) Find f(2) b) Find f(­4) c) Find f(a+b) Sep 9 ­ 12:17 PM 13 2­1 Relations and Functions 2010 September 10, 2010 Homework pg. 59 ­ 60 #'s: 12 ­ 54 even, 62 ­ 65 Sep 12 ­ 9:05 AM 14