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College Algebra Name: Guided Notes – Sec 1.1 Period: 3 5 Date: 8/24/10 Relation – a pairing of the elements of one set with the elements of a second set, generally written as a set of ordered pairs Abscissa – the first element of an ordered pair Domain – the set of all first elements (abscissas) in a given relation (set of ordered pairs) Ordinate – the second element of an ordered pair Range – the set of all second elements (ordinates) in a given relation (set of ordered pairs) Example #1 – Rewrite the following set of data as a set of ordered pairs. Then identify the domain and range. Windchill Factors at 20o F Wind Speed (mph) Windchill Temp (o F) 5 10 15 20 25 30 19 3 -5 - 10 - 15 - 18 Relation: { (5, 19) , (10, 3) , (15, - 5) , (20, - 10) , (25, - 15) , (30, - 18) } Domain: { 5, 10, 15, 20, 25, 30 } Range: { 19, 3, –5, –10, –15, –18 } Example #2: Rewrite the following relation as a set of ordered pairs. Then identify the domain and range. The domain of the relation is all integers from – 2 to 2, inclusive. The range of the relation is 2 less than twice each member of the domain. First, identify the domain. D = { - 2, - 1, 0, 1, 2 } Next, identify the range. Note: It may be helpful to set up a table of values. x -2 y = 2x – 2 = 2(-2) – 2 = - 6 -1 = 2(-1) – 2 = - 4 Thus, the range is … 0 = 2(0) – 2 = - 2 R = { - 6, - 4, - 2, 0, 2 } 1 = 2(1) – 2 = 0 2 = 2(2) – 2 = 2 That means the relation is the set of ordered pairs … { (- 2, - 6) , (- 1, - 4) , (0, - 2) , (1, 0) , (2, 2) } Example #3: Determine the domain and range for each of the following relations. 1. 2. 3. 4. Each mark represents 5 units D= D= All reals R= D= All reals R= All reals #>0 D= –5 < # < 5 All reals R= –5 < # < 5 R= #>0 How do graphs 3 and 4 “differ” from graphs 1 and 2? Note: Think of your answer in terms of domain and/or range. - In 3 and 4, there are values of the domain that … are paired with more than one value of the range. - In 1 and 2, the values of the domain … never appear more than one time. - In 3 and 4, you can draw vertical line(s) that … intersect the graph in more than one point. - In 1 and 2, you can draw vertical line(s) that … never intersect the graph in more than one point. What term can we use to describe the relations represented by the graphs in 1 and 2? They represent functions. Define a Function – A function is a relation in which each element of the domain is paired with exactly one element of the range. Ex. #3 - Determine whether each relation is a function. { (1, 2) , (2, 3) , (3, 4) } D= R= {1, 2, 3} {2, 3, 4} Function: Y N Yes {1} Function: Y N Yes { (1, 1) , (2, 1) , (3, 1) } D= R= {1, 2, 3} { (1, 1) , (1, 2) , (1, 3) } D= R= {1} Function: Y {1, 2, 3} N No This tells us that in a function … - No element of the domain … can be repeated. - Elements of the range … may be repeated. - If there are fewer elements in the domain then there are in the range, then … the relation is NOT a function.