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by: Patrick Esguerra

WeekThreeAlgebraNotes.pdf 20045

Marketplace > Ohio State University > 20045 > WeekThreeAlgebraNotes pdf
Patrick Esguerra
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This 6 page Reader was uploaded by Patrick Esguerra on Friday January 30, 2015. The Reader belongs to 20045 at Ohio State University taught by in Winter2015. Since its upload, it has received 27 views.


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Date Created: 01/30/15
1272015 Recitation Difference Quotient fx4X5 a b C d 23 fxh4x4h5 fXhfXh 4X4h54X5h 4hh H4 provided that hi0 Composition Given functions f and g f o gXfgX 3 If fXX2l and gXX2X find the following a fgXfXgXX21X2X2X2X1 13 fgXfXgXX21X2X X1 c f g 12f 12 g 12 122 1 122 12 12 Alternately Plug 12 into solution b 12 1 12 d fgXfXgXX2 lX2X X4X3 X2 X Careful fg fg fgifo g e f g h fgXfXgXX21X2XX1X1XX1 X 1X provided that X7 1 fg l2 12 l 12 32 12 32 213 f O gX fgXX2X21 X2XX2X1 X4X3X3X21 42X3X21X4X2 g 0 fXgfXX212X21X21X21X21 X4X2X21X21 X42X21X21 X4X2 i g0 f33432 81 972 Lecture 23 Given KX Xl 0 Find 2 non identity functions such that k f o g Fltxgt v00 gltxgtx1 Problems Find functions f amp g such that hXfgX 16 hX 23X53X522 0 Find non identitv functions f and g such that h f o g FXfgX o FX2XX22 o GX3X 5 o FgX23X53X522 25 Function 1 inputl output 0 Use the vertical line test to check if a graph is a function If the vertical line intercepts with the graph in more than two points for example if the graph resembles a heart then it s not a function 1 29 20 l 5 Recitation Chapter Two Review 0 Domains 0 Difference Quotients 0 Composition Domains If f is a function the domain of f is every possible inputwhichever X where fX makes sense 0 Example 1 X o fX X f4 V42 f100 10010 f0 00 f 1 1Undefined o DomainXZO o 2 fXlX l o FXlX l o F1lOUndefined 0 Domain X7 l00 oo 0000 21 12 gX V4x3 0 4X3ZO 0 4XZ 3 o XZ 34 0 Domain XZ 34 14 IXX5X2X6 O X2X6O O X3X 2O O X 3 X22 0 Domain X753 X 2 Difference Quotient Given fX fXh fXh 1302015 Lecture Straight lines have constant slopes o The slope of a straight line is called rise over run Slope Y239Y1X2X1 0 You can also get the slope with yi y2X1 X2 Example Find slope of line joining points l4 and 38 Slope 8 43 1441 Slope of horizontal line 0 OX Slope of vertical line Unde ned 000 Equations of straight lines given 2 points Example Xlyl and X2y2 Find slope my2 y1X2 X1 Pointslope Formula for a liney y1mX X1 Find equation of line through 13 and 85 Step One Find slope m538129 Step Two yylmXX1 If you use 13 as the point you have y329X1 O Y 3 29X29 o Y 29X293 o Y 29X299 YmXb is called the SlopeIntercept Form for a straight line Example Put this equation of a line in slopeintercept form 9X7y10 7y 9X 1 Y 97X17 Slope 97 yintercept 0 17 Parallel and Perpendicular Line Parallel lines have the same slope Example Find the equation of the line M parallel to given line L with equation 5X 2y80 and passing through the point 13 0 Step One Find the slope of given line L O 5X 2y80 O 5X822y2 O Y52X4 Slope of line L is 52 0 Step Two Use point slope form for finding equation of line M O y y1mX X1 O m52 X1y113 O Answery 352X 1 o Y 352X 52 o Y52X 523 o Y52X12 Perpendicular lines are lines that intersect so that they form a right angle Rule You get a perpendicular slope with the formula m1m21 I M21m1 Example Find equation of line N perpendicular to L through the point 17 Equation of line L is y52X4 Slope of line L is 52 So slope of line N is l52 25 Equation of line L is y 7 25X l SlopeIntercept Form y 25X375


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