### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Elementary Algebra MTH 070

Chemeketa Community College

GPA 3.98

### View Full Document

## 42

## 0

## Popular in Course

## Popular in Mathematics (M)

This 17 page Class Notes was uploaded by Jess Ruecker on Monday October 5, 2015. The Class Notes belongs to MTH 070 at Chemeketa Community College taught by Staff in Fall. Since its upload, it has received 42 views. For similar materials see /class/219421/mth-070-chemeketa-community-college in Mathematics (M) at Chemeketa Community College.

## Similar to MTH 070 at Chemeketa Community College

## Reviews for Elementary Algebra

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/05/15

Graphing Calculator Graphing with the TI86 I Introduction The TI86 has fty keys many of which perform multiple functions when used in combination Each key has a symbol printed on its face When a key is pressed the calculator does whatever is printed on the face of the key This is o en referred to as the primary function of the key For example the primary function of the ON key is to turn the calculator on the key performs addition and x2 raises numbers to the second power In addition to their primary functions many keys have second or shi ed functions These are the symbols written in yellow and blue above the keys To have the calculator do what is written in yellow you must rst press the 2nd yellow key To type letters into the calculator you must rst press the ALPHA blue key II Plotting Points in a Scattergram We can use the calculator to create a scattergram of the data displayed in the table at right As you follow the steps below compare the screen on your calculator to the screenshots to the right Press 2nd then STAT STAT is a shifted function press 2nd then the key Your calculator window should look like the picture at the right anc I 0quot I PLM Innnul van gt Press the F2 EDIT key If you have any numbers data in the lists xStat yStat or fStat you can clear them by pressing the up arrow A to move the cursor to the top of the column then press the CLEAR key followed by ENTER Use or to get to the next list and repeat the steps to clear all the lists To enter the new data enter the Xvalues from the table in xStat by typing 2 ENTER 5 ENTER 8 ENTER 11 ENTER Move the cursor to yStat and enter the Yvalues 25 28 58 and 130 in the same way In the Shit column enter 4 ones that is a one for each data pair To get to the plot menu rst press 2nd then STAT Press PLOT F3 to bring up the plot menu MLC MTH 070 Graphing With the Tl86 Press F1 PLOT1 then ENTER to turn Plot 1 on Note that Type Xlist Ylist and Mark should all be set the same as the picture at the right The Type shown is scattergram the data list uses xStat for the Xvalues yStat for the Yvalues and the points will be plotted as little squares as indicated by Mark Press GRAPH to bring up the graphing menu To adjust the window so that all the data points are in view we use a feature called ZDATA or zoom data To nd that feature rst press ZOOM F3 A submenu pops up below the zoom menu Press MORE to advance the submenu to more choices Press ZDATA F5 This sets the window to t the data points Press EXIT This removes one ofthe popup menus so that all the points in the scattergram become visible III Entering an equation Begin by pressing the GRAPH key The GRAPH menu appears on the screen and gives the following options x WIND ZOOM TRACE GRAPH These options are accessed by pressing the F keys located in the top row of keys Notice the arrow to the right of GRAPH on the screen This arrow indicates there are more options Note the x and yaxes may appear on the screen If they do ignore them for now MLC1M5 02093008 OPP sPeEL Xlist NamexStat Vlist NamesStat Mark Han HTITIII that mun l mlrnn ra i maa MLC MTH 070 Graphing With the TI86 Press the MORE key to see more onscreen menu options Notice the arrow to the right of the RCDGB menu option This means there are even more options Press the MORE key to see the remaining menu options Press MORE again to return to the original menu options Select yx by pressing F1 the ashing rectangle next to y1 is called the cursor The cursor indicates where characters will appear when a key is pressed If there are expressions next to any of the y1 use the V key to move the cursor to the line containing the expression and press CLEAR Repeat as needed Now with the cursor at y1 enter 2x5 Use the xVAR key or F1 to enter the variable x IV Displaying Values in a Table We can use a calculator to display a table of values for an equation that has been entered into the calculator Press the TABLE button Now press TBLST F2 to set up the table TblStaIt is the rst input value in the table and ATM is the increment for the input values Enter 2 for TblStaIt be sure to use the key and press ENTER Then enter 3 for ATM and press ENTER Now press F1 to display the table Notice that the x values start at 2 and increase by an increment of 3 These are the instructions that you gave the calculator in the previous window You can scroll up or down the table using A or V MLCrMSu 08093008 I I EunLl THclnrHcl I I 11339 I NIND I EDEIM mm v Inmwn Hui New PWB 51I m HINIII EDEN1 TFir39IIZE IEFIIIFH nnmm mu Hot Hot HIE2X5 ma HINII aunt1 mat EHHPH IIImm A P1ot1 Hot P103 3152 X5I IT BLEITBLSTI I I I THBLE SETUP TblStaPt 392 Tbl3 I dpnt mm Fisk ITRBLEI I I I I MLC MTH 070 Graphing With the TI86 V Graphing an Equation Press M3 2nd F3 to select the ZOOM menu then select ZSTD by pressing F4 You should get the graph of y 2x 5 The ZSTD command tells the calculator to graph the equation in the standard screen The standard screen includes the xaXis from 710 to 10 and the y aXis from 710 to 10 Verify this by pressing F2 to get WIND This is the WINDOW screen Xscll means the xaXis is scaled so that each mark is one unit Notice the yaXis is also scaled with one mark representing one unit Press TRACE F4 The calculator places the cursor on the graph ofthe line y 2x 5 The number 1 in the upper right comer ofthe screen indicates the number of the equation being traced y1 in this example Move the cursor along the line by pressing or Notice at the bottom of the screen the coordinates of the cursor are indicated by X and Y VI Using Intersect to Solve an Equation We can use the Intersect feature on the calculator to solve the equation 3x 7 5 Go to the yx window by pressing GRAPH and yx Fl If necessary clear out any equations and turn plots off Enter 3x 7 in y1 and enter 5 in y2 To see the graph press 2nd GRAPH F5 Notice the graph of y1 is a straight line with a slope of 3 and y2 is a horizontal line To find the point of intersection of the two lines press MORE Press MATH Fl MLCrMSu 08093008 Hot Hot Hot H1EIX5 wIHDDw XM1nIIB xMax1B x5911 HM1n391B HMax1B x x 95 F10 Plot Plot Hll m Nan ZUDM THREE lifi F39H minim PM PML Z PHI 395 K39 HZE5I ME MIND E IJH TERIIE IEFIFIF H nnmm m I lJ Fl39lFiH MLC MTH 070 Graphing With the Tl86 5 Press MORE Press ISECT F3 rirstcurue xn The cursor appears on one of the graphs You can tell which one by looking at the number in the upper right corner The calculator rompts you to tell it which two graphs curves you are nding the intersection of Press ENTER to indicate that the cursor is on one gggondcme f your curves The cursor jumps to the other graph and prompts you with Second curve Press ENTER to indicate that the cursor is on the other curve Guess xn Now the prompt is Guess which is asking you to lace the cursor near the point of intersection Use the and keys to f move the cursor close to the point of intersection and ress ENTER The cursor jumps to the point of intersection and the coordinates of that point are indicated along the bottom of the screen Intersection x VII Linear Regression Using the data in the table at the right we ll use the calculator s linear regression feature to nd a linear equation that best ts the data First we need to enter the data into the stat lists If you need to re esh your memory on how this is done go to section II of this supplement and follow the rst four steps of Plotting Points in a Scattergram When the data has been correctly entered your screen should look like the picture at the right Press EXIT to retum to the home screen then press CLEAR MLC1M5 02093008 MLC MTH 070 Graphing With the Tl86 To perform the linear regression function rst press 2nd then the STAT k ey We Want to perform a calculation on the data so press CALC F1 Select LinR F3 to perform a linear regression Note there are other types of regression besides linear In this Window the options 39nclude exponential regression Epr F5 and quadratic regression MORE P2Reg F4 among others Press ENTERto perform the regression This output describes a linear equation with slope 115 and yintercept l45 so the equation is y 115x7145 We are not going to use the corr for our purposes To graph the regression equation along with the scattergram rst plot the scattergram y turning on plot 1 and pressing GRAP ZOOM MORE then ZDATA F5 If you need to refresh your memory on these steps go to section II Plotting Points in a Scattergmm and read steps 5 through 8 Pressyx Be sure that all equations are cleared and the plot is turned on When We perform regression the equation is stored as a statistics variable named RegEQ We graph the regression equation by inserting RegEQ into the y Window First to nd RegEQ press 2nd then CATLG VARS CUSTOM Press the MORE key twice Press STAT F4 MLCM39MISn nznyannz anc I EDII I PLI II Innnul van gt li39m rIr rLnr rumI CFITFILDGUFIRIFIBLE canGI nLL IRE L I FL I Ll r gt CFITFILUEiUHR I FIBLE mam nk I m I rnr lumn MLC MTH 070 Graphing With the TI86 7 Select RegEQ by pressing the down arrow key V four times 39lP1 HlERegEq Press ENTER This inserts the regression equation into the yx screen for grap 39 g m Han nnrI Inn5 Izmiru IIImm Press 2nd then GRAPH FS We can see the regression line along With the scattergram of the data VIII Finding the x intercepts of a graph Clear the previous equations and enter the equation y x2 7 x7 6 Graph the equation Be sure the Window is set so that you can see all of the xintercepts In this example use the standard Window 900 I mun In In Irmczlamm Press MORE then MATH F1 We are looking for the x intercepts ofa quadratic Which are also called roots Press ROOT F1 The calculator will only look for one xintercept at a time and 1t Notice that the cursor is ashing on the screen at the point 06 will only look for one Within a range of x values that you must Eksound m specify Left Bound on the screen is a prompt for you to enter the smallest x value in the range Use to move the cursor to the le ofthe le most xintercept and i press ENTER The rightpointing black triangle on the screen indicates the smallest x value the calculator will consider in looking for an xintercept Right Bound on the screen is a prompt for you to enter the largest x value in the range Rishtkound xz3abssz3a1 203915EEEZIX Use to move the cursor to the right of the le most xintercept l and press ENTER The le pointing black triangle on the screen indicates the largest x value the calculator will consider in looking for an xintercept You should have placed the le and right bounds to that there is one and only one xintercept between the mmmsn nxmannux Gum Z39l55301557 135317zoaa MLC MTH 070 Graphing With the TI86 triangles horizontally Guess is a prompt for an x value in the specified range that the calculator can use to start its search algorithm Any x value in the range will work If you press ENTER the i calculator will use the x coordinate of the current position of nnnr the cursor Since the cursor is at the right bound that value is 1quot valid Press ENTER The cursor is ashing on the x intercept and its coordinates are listed at the bottom of the screen 20 Repeat the procedure to nd the other xintercept IX Problems for Practice Use a calculator to make a scattergram of each of the following data tables 1 2 X X Use a calculator to make a table of values for the following equations Use TblStart 10 and ATbl5 3 y3x2 4 y x4 Use a calculator to draw the graphs of the following equations 5 y32 x 6 y52x l gt1 Use the Intersect feature to solve the equation 2x 3 4 9 Find the point of intersection of the graphs of y 5x l and y 2x 3 gt0 Use linear regression to find a model of best fit equation for each of the tables Graph the regression model and the scattergram in the same window Round decimals to two places a b X MLCrMSu 08093008 MLC WHWUGupl39nnng39hzTLX 9 m Fmd39hzxrxmuceplsufyx139x727 9 s y755xr359 b ynsx445 Graphing Calculator Graphing with the TI83 PlusTI84 Plus I Introduction The TI84 Plus graphing calculator has greater memory capacity is faster and has a higher contrast screen than the TI83 Plus model Aside from these differences the two calculators have virtually the same keyboards and they are keystrokeforkeystroke compatible This is also true of the older TI83 and TI84 models All TI83 and 84 models have fty keys many ofwhich perform multiple functions when used in combination Each key has a symbol printed on its face When a key is pressed the calculator does whatever is printed on the face of the key This is o en referred to as the primary function of the key For example the primary function of the ON key is to turn the calculator on the key performs addition and x2 raises numbers to the second power In addition to their primary functions many keys have second or shifted functions These are the symbols written in yellow and green above the keys To have the calculator do what is written in yellow you must rst press the 2nd yellow key To type letters into the calculator you must rst press the ALPHA green key II Plotting Points in a Scattergram We can use the calculator to create a scattergram of the data displayed in the table at right As you follow the steps below compare the screen on your calculator to the screenshots to the right Press the STAT key Your calculator window should look like the picture at the right SetUPEditor Press 1 Edit If you have any numbers data in the lists L1 L2 or L3 etc you can clear them by pressing the up arrow A to move the cursor to LZIL3 the top of the column then press the CLEAR key followed by ENTER Use or to get to the next list and repeat the steps to clear all the lists NOTE ifyou press DEL instead of CLEAR the entire column will vanish Ifyou do this mm by accident pres STAT 5 SetUpEditor then ENTER to replace the deleted column 1 L2 L3 2 To enter the new data press the STAT key then 1 Edit Enter the X g g values from the table in L1 by typing 2 ENTER 5 ENTER 8 ENTER 11 Ir 3 ENTER Move the cursor to L2 and enter the Yvalues 25 28 58 and 130 quotquot 39 in the same way L2t5 Now press the Y key If you have any equations on this screen press CLEAR Use the A and V keys to move from Y1 to Y2 andYs etc and press CLEAR to remove all equations xxxxxx Next press 2nd then STAT PDOT MLC MTI I 070 Graphing With me Tl83Tl84 Press 1 to select Plot 1 then Press ENTER to turn Plot 1 on Note that Type Xlist Ylist and Mark should all be set the same as the picture at the right The Type shown is scattergrarn the data list uses L1 for the X values L2 for the Yvalues and the points Will be plotted as little squares as indicated by Mark Finally to see the scattergrarn press ZOOM then press ZoomStat 9 ZoomStat automatically adjusts the calculator Window so that all the points in the scattergrarn are visible III Entering an equation We use the top row of keys for graphing they are Y WINDOW ZOOM TRACE GRAPH Start by pressing Y The ashing rectangle next to Y1 is called the cursor The cursor indicates Where characters Will appear When a key is pressed If there are expressions next to any of the Y use the V to move the cursor to the line containing the expression and press C LEAR Now With the cursor at Y1 enter 2x 5 Use the XT9n key to enter the variable x IV Displaying Values in a Table We can use a calculator to display a table of values for an equation that has been entered into the calculator Press 2nd then TBLSET the WINDOW button to set up the table TblStart is the rst input value in the table and ATM is the increment for the input values Enter 72 for TblStart be sure to use the 7 key and press ENTER Then enter 3 for ATM and press ENTER Press 2nd then TABLE the GRAPH button Notice that the x values start at 72 and increase by an increment of 3 These are the instructions that you gave the calculator in the previous Window You can scroll up or down the table using A or v mumsmmesz Plotz not OFF HP Hmrrwu Hm 1I V V V V V V7 run rwn H S ViE2X5I I Tbl Start 39 4Tb13 lndPnLE c 3555 MLC MTH 070 Graphing With the TI83TI84 3 V Graphing an Equation Press ZOOM Notice there are many options under the ZOOM menu 2 Select ZStandard by pressing 6 You should get the graph of J y 2x 5 The ZStandard command tells the calculator to graph the equation in the standard screen I The standard screen includes the x aXis from 710 to 10 and the y aXis HINDUle from 710 to 10 Verify this by pressing WINDOW Xscll means the xaXis is scaled so that each mark is one unit Notice the yaXis is also scaled with one mark representing one unit Xres1 is the resolution maxfl39a 561 1 sett1ng and should usually be left at l Xres1 Press TRACE The calculator places the cursor on the graph of the line waxes y 2x 5 The equation written in the upper left comer of the screen 4 indicates what equation has been graphed Move the cursor along the line by pressing or Notice at the bottom of the screen the coordinates of the cursor are indicated by X and Y 9G 391fll 333 2B23HD391 VI Using Intersect to Solve an Equation a Phtaivg lat Hot d W1 We can use the Intersect feature on the calculator to solve the equation 3x 7 5 In the Y screen enter the equation Y1 3x 7 and Y2 5 VE W 39 To see the graph press GRAPH Notice the graph of Y lis a straight line If with a slope of 3 and the graph of Y2 is a horizontal line Press 2nd III then CALC F4 Ifquot To find the point of intersection of the two lines press intersect 5 maximum 1ntersect dHdx IFthdx MLcrMSu 08092608 MLC MTH 070 Graphing Wilh Ihe TI83I39I84 4 135P The cursor appears on one of the graphs You can tell which one by looking at the u per left comer The calculator prompts you to tell it which two graphs curves you are nding the intersection of Press ENTER to indicate that the cursor is on one ofyour curves rimcwm 30 39 25 The cursor jumps to the other graph and prompts you with Second curve Press ENTER to indicate that the cursor is on the other curve Second curv 0 2 5 Now the prompt is Guess which is asking ou to place the cursor 25 near the point of intersection Use the and keys to move the cursor close to the point of intersection Guess 30 5 press ENTER The cursor jumps to the point of intersection and the coordinates of that point are indicated along the bottom of the screen Intersection H 5 VII Linear Regression Using the data in the table at the right we ll use the calculator s linear regression feature to find a linear equation that best fits the data First we need to enter the data into the stat lists If you need to refresh your memory on this is done go to section II ofthis supplement and follow the first four steps of Plotting Points in a Scattergram ll 25 When the data has been correctly entered your screen should look like E5 the picture at the right To perform the linear regression function first press the STAT key 5 UK ECLisL SetUPEdltor We want to perform a calculation on the data so press the right arrow to CALC lDuarLRaQ menuSn ownsDE MLC MTH 070 Graphing With the Tl83TISit Select LinReg 4 to perform a linear regression Note there are other pes ofregression besides linear In this window the o tions include quadrch regression QuadReg 6 and exponential regression Epreg 0 among others Press ENTER to perform the regression This output describes a linear equation with slope 115 and yintercept 145 so the equation is y 115x7145 We are not going to use the r2 or r for our purposes Don t worry ifyour calculator does not show these values To graph the regression equation along with the scattergmm rst plot the scattergrarn y 39 on plot 1 and pressing ZOOM then Zoomstat 9 Ifyou need to refresh your memory on these steps go to section II Plotting Points in a Scattergram and read steps 5 through 10 Press Y Be sure that all equations are cleared and the plot is turned on When we perform regression the equation is stored as a statistics variable named RegEQ We graph the regression equation by inserting RegEQ into the y window First to nd RegEQ press the VARS key Since RegEQ is a statistics variable select Statistics 5 by pressing 5 iegEQ is an equation so select EQ by pressing the right arrow twice Select RegEQ by pressing 1 or ENTER This inserts the regression equation into the y screen for grap 39 MLCTMSn TIEEmma 1nHeg axbJ I m Motz Plot V15115X39145 sz V W MLC MTH 070 Graphing With the TI83Tl 84 Press GRAPH We can see the regression line along with the scattergram of the data VIII Finding the xintercepts of a graph Turn off plots and clear the previous equations and enter the equation 2 y x 7 x 7 6 Gmph the equation Be sure the Window is set so that you can see all of the xintercepts In this example use the standard Window Press 2nd then CALC the TRACE button The menu under CALCULATE has several options We are looking for the zero values so press 2 The cursor is ashing on the graph at the point 076 The calculator will only look for one xintercept at a time and it Will only look for one a range ofx values that you must specify Left Bound on the screen is a prompt for you to enter the smallest x value in the mnge Use to move the cursor to the le of the le most xintercept and an xintercept Right Bound on the screen is a prompt for you to enter the largest x value in the range Use to move the cursor to the right of the le most xintercept and press ENTER The le pointing black triangle on the screen indicates the largest x value the calculator will consider in looking for an x intercept You should have placed the le and right bounds to that there is one and only one xintercept between the triangles horizontally mams omwsm Iou Plotz not xxxxx 3 1 5 5 7 unsound xn 1x2xs Kl l uess x1 aszsz 2252m MLC39 MTH U70 Graphing With the TI83TI84 calculator can use to start its search algorithm Any xvalue in the range will work If you press ENTER the calculator will use the x Guess is a prompt for an x value in the speci ed range that the I coordinate of the current position of the cursor Since the cursor is at the right bound that value is valid Press ENTER The cursor is 32 0 ashing on the xintercept and its coordinates are listed at the bottom of the screen 720 Repeat the procedure to nd the other xintercept 4 HE IX Problems for Practice Use a calculator to make a scattergram of each ofthe following data tables 2 Use a calculator to make a table of values for the following equations Use TblStart 10 and ATbl5 3 y3x2 4 y39 x4 Use a calculator to draw the graphs of the following equations 3 7 5 2x 7 1 gt1 Use the Intersect feature to solve the equation 2x7 3 4 Find the point of intersection of the graphs of y 5x l and y 72x 3 9 Use linear regression to nd a model of best t equation for each of the tables Graph the regression model and the scattergmm in the same window Round decimals to two places a b 10 Find the xintercepts of y x2 39x7 27 MLC 39MSn mug26m MLC MTH 070 Graphing With me TI83TI84 Answers standard Window 1 2 3 u WI 25 s 13 a 2 s 17 m 32 15 w a an 52 18 4 5 6 7 9635 y4 8 9 a 755x7359 b 115x7145 mmwion 1571st 2 as H u5 a s 0 mnwsmxmwmx

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.