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# R.3 Finding Domain and Range STAT 1102 - 003

Temple

GPA 3.11

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This 4 page Class Notes was uploaded by Kayla Notetaker on Monday September 21, 2015. The Class Notes belongs to STAT 1102 - 003 at Temple University taught by Ron Kershner in Fall 2015. Since its upload, it has received 52 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.

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Date Created: 09/21/15

R3 Lecture Notes Professor Kershner Types of Notation Set notation x ls xS 5 Read as A set of all X values between 1 and five that includes 1 and 5 XI 3ltxlt10 This is read as A set of all X values between 3 and 10 but does not include 3 and 10 Q remember that SAZ mean that the number is included greater than or equal toless than or equal to O on a number line these are denoted by a closed circle 0 lt or gt mean that the numbers are NOT included in the interval greater than essthan O on a number line these are denoted by an open circle Union of sets A union of sets is the outcome from two or more events together Denoted by a U AUB means all elements in set A or B using sets from above x 13x35 and XI 3ltxlt10 Let the first set be event A and the second set become event B AUB x ISxlt10 because AUB asks for all possible outcomes resulting from event A happening OR event B and because event A is all X values between 15 B is all X values between 310 and these two intervals overlap they can be written as x ISxlt10 Intersection of Sets An intersection is two or more outcomes that occur together Denoted by symbol n AnB all elements in BOTH A and B AnB x 3ltxSS Why Event A AND event B must both happen in order for an intersection Between the interval 3 lt X s 5 both event A lSXS5 and event B 3 lt X lt10 occur Interval Notation Open Intervals Using the same events from above B XI 3ltxlt10 would be an open interval MEANING the beginning and end numbers of the interval are NOT included How do we right this Using parenthesis 3 10 OR using lt gt symbols when writing interval with a variable in between 3 lt X lt 10 Closed Intervals These are the opposite of open intervals Using event A from above XI 13x3 5 the s and 2 symbol mean that 1 and 5 are included in the interval why because these symbols mean greater than or EQUAL TO and less than or EQUAL TO so we MUST included 1 and 5 within the interval Written using brackets 1 5 Using 5 and 2 symbol and a variable this is written 1 s X s 5 Half Open Using the example above when nding An B events in BOTH event A and B the interval was X 3ltxSS this can be written as 3 5 because 3 is NOT included in the interval so we use but 5 is included so we use when including X this is written 3 lt X s 5 Any event that is unbounded on the left or right can be written as 00 b unbounded on the left goes on to the left forever a 00 unbounded on the right goes on to the right forever Unbounded on the left and right would not be a set 00 00 This would be the entire real line all X values Summary of Terminology for Intervals 1 Roster list individual numbers a Uses and b if the set of number 3 5 6 810 c Roster notation 356810 2 Interval ah ah abl lab depends on whether or not a or b is included in the interval 939 3 Set a X I a lt X lt b can exclude numbers using this notation i XX is a real number and X 7 3 ii X is a real number not including 3 iii in otherwords 00 3 U 3 0 0quot lt Parenthesis on 3 indicate 3 is NOT included in number line FOR KERSHNER S CLASS UNLESS DIRECTED OTHERWISE FOR HW QUIZZES OR TESTS USE INTERVAL NOTATION Finding Domain and Range Graphical Approach Domain 4 3 all x values brackets used because circles are closed RangeL54 all y values brackets used because circles are closed Domain 4 4 Domain is bracketed because where was open circle is there is a closed circle so the number is included in domain Range 1 2 3 4 why roster notation these are y values specific to each function on the graph it does not climb continuously but has a specific point Finding domain algebraically Rational functions 1 set hx to zero 2 solve for x 3 why because any numberO does not exist Example x30 subtract 3 from both sides X 3 domain xlx is a real number and X 7 3 Functions with Radicals 1le 1 set gx 2 O 2 solve for x 3 if K is not given assume k2 4 Why because you can t square root a negative number Example fltxgtVEI 1 restrict domain 2 add two to both sides x22 Domain xlx 2 2 x is a real number greater than or equal to 2 2 00 2 s x lt oo

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