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# Obj 5-Obj 7c MAC1105

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This 7 page Class Notes was uploaded by Michaela Maynard on Tuesday September 29, 2015. The Class Notes belongs to MAC1105 at Florida State University taught by Pennington LeNoir in Summer 2015. Since its upload, it has received 51 views. For similar materials see College Algebra in Calculus and Pre Calculus at Florida State University.

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Date Created: 09/29/15

0 a Solve 4 x 5 Solve sz 6 1 2 7M squarerooe c an 30 Apgxs gb W Cannot be M 15 p X A OM NO Son 70 3mmth Solve V211 3 x 39 Edutmhl Solve10 41 O KzaHXL39H 0K X aquotLIL HL La 39039 KL 0 9x27xcp XXO K49 0 X l50 X DO X XLo Two somth CHIS 539 Objective 5 Linear Inequalities Interval Notatation And and Or Obj 5b Interval Notation Used to represent the solution to inequalities Please Note Inequalities are easier to read if the variable is on the l Interval Notation is always written in pang QCY Iln C QfC er ellb 37 rl htgt 37231 353732 Not mama CndPOMb Brawetr usmg empo t Express in interval notation ya I ntcr va N at a b in an S quot 2 a 4 3 00 3 2 gltx 1 X gta M 9 0 qR 39239 gt x gt 0 M 0 O S Llt Z Cy 20 Obj 5c The math terms And and Or Plan of Attack Draw a picture of the two sets on a number line then check if And or Or HIM OR means UYhOh AND means lVl39thS fCt39th Combme cvef thmg over MP Express in interval notation 3 S a and a gt 5 gt gt 5323 02d 5 Hmwcr 5 co HE A 3 5 Express in interval notation x Z 3m lt 5 m HmSw r 3 5 rc tm 5393 lt 0h 5 bc not i 3 5 Ineluoled In both xi Express in interval notation a 2 3am lt 5 My 1 I I A Rh3 J V I l 3 5 Express in interval notation cc 3 3x gt 5 Pom union 0 dudmmt 5913 6 3 w9 4 i i 3 Hn5 w3U5 gt 3 5 Express in interval notation 1 lt 3 gt 5 llv HWO wftttfn quot3 quot 3 over r thW er f i i 339 E 3 3 6 21 Q EVnVUj 36 6quot Obj 5a Solve Linear Inequalities 9 Plan of Attack Like Linear Equations Remove grouping symbols Collect like terms Isolate variable W Unlike Linear Equations If you ever multiply or divide by a negative number must I CMC 5 the inequality sign Inequalities are easier to read if the variable is on the Qt Solve 2 2a 6 Z 4a 5 12 Solve 5 lt 6 2x 1 S 4 T iquahtles 07 9W0 3 lJLROHa 54O azxquotR Ll 2x40 139 II5 8 54 9393 5 4 45 gt 8 aquax om mega H l H5m2awml gtLzo gto x4quota 5 l e Il 4 X org 0 az E0 9 Solve5gt1 zgt15m Solve 26 3mlt2x 1lt9 3a 5Nquot 7316 AND lquotaLgtLS3a 3235 33quot mm 07X 4l 43x 07 15 Zx gt3o3p 854 5544 3 a gt30HUL Sr x cquot 1 337 4 555 ASD X40 34 K Eng Xgt X z 393 a 158 4 P I aquot v d 1 Objective Rectang7ular Coordinate System Distance and MidPoint Formulas Obj 6a Rectangular Coordinate System The notation PI y is used to refer to a point in the coordinate plane It is an BYdfer 039 P101 37 quot 3 O 67 A B C D 22 Obj 6b Distance Formula d K sz r ya 339 a 7 d CX R L 3 33 MQMOHZC For Mu ta Find the distance between the points P1 12 and Q3 4 d 3 ti L Amiga 34 3 gm JEWU 5 N 539 A 7F MuH CIAOICC 2 quot 33 Find the distance between the points P 4 4 and Q8 13 a 39 3 d 5 X W39DK CW 3941 a 4 Jo a 502 2 mam Obj 6c MidPoint Formula 56 Til2 t f ji a gt a 1d a aMule Chmcc Find the mid int of the line segment joining P3 2 and Q 7 1 0 2 A 0 O 4 v 1 w g Find the midpoint of the line segment joining P a 0 and Q0 W igs 13953 so oi 23 Obj 7 General Graphing Principles Obj 7a Point on a graph If a b is on the graph of an W a relationship between x andv then when ll 3 a and j 7quot b the equation is Plan of Attack ll it in glue Vb Y J If 6 c is on the graph of y2 cc 3 nd the value of c Gazar3 A CRQ Mult l t I C 39 quot 3 Chmd If c 27 is on the graph of 93 y 3 nd the value of c Q3 THE 3 La44 sz gm Obj 7 b Intercepts Intercepts Points Where a graph Ly or WUCh 63 a coordinate axis Listntercepts for each graph 5 XX WWD39 e 202 ya We 39 5WWV Com th 52C L 2 2 3 539 IV 5 mom 6 m 39 quotll Find all intercepts algebraically Plan of Attack For xintercepts let quot O solve for cc For yintercepts let LCD solve for y Find all intercepts xy3y20 3 4 2 0 A 3 a 39T and wt let Kcogo r 5 a a 0 IT 591ml 1 ma a 34gt a Jemima 0 y 390 0gtOgt 30 OY a 3M 0 339 m Lia bMCC b quot WV A 0quot L Find all intercepts 512 333 27 MI X Int39 oar sisa7 x Mo m 333a7 a 5eQ Xaz39a l y 3 q A 4 L7IQ A I gate m2 Obj 7c Symmetry Symmetry with respect to raxis To test algebraically replace a ULth neg y le 3 g 33 quotKSee if an equivalent equation results a Symmetry with respect to gzaxis ya To test algebraically ware lb wmh 0133 1401 39 39quot 53 4k See if an equivalent equation results 3 Symmetry with respect to Origin To test algebraically replace so WWH htj zC M EL 1 d b with j quotL1 7 99 Glqu39DE 9 An 39 example of one type of Symmetry problem If 3 6 is a point on the graph of a elation equation with a and y that is symmetric with respect to the xaxg which of these must also be on the graph 3 6 3 3 6 the h over 51 quot ee if an equivalent equation results gL v ge r 0 m 53 l 5 Test for Symm wrt Origin y x2y3cc xax T525 312161 6 both a 33ca 5 3 4963 LU 3gt gtquot 393 2 WW Test for Symm wrt yaxis xzy 32 3 Tat 1619mm x w 56 a 2 y z 3 W C 33 Cf s gt6 5 3 32 7 13 0 av o y k 5 BUWWMCCWC w aspect bD y39all5 Test for Symm wrt Origin 33 gm h 09 if 3 3 SaMMEWm wrt cm x21 3915 vmace both a w y 3 l39 65gt n H gt a T3 33 LCOM39PGVC to 06an L H 00 6H 0quot 831 3 3 W b An online example Which of the following is symm wrt the xaxis 2 ygs 2 y2f5x 3 L a s L3 5 13 gx j SMME hc Ofi ln m2y25 x4y3 2y2y5 6 o395 Lquot 6353a3932 393 5 30 3 46 U 3 02 3 5 3 5 3N5 26

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