Texas Instruments TI-84 Plus Silver Edition, Manual

Page 1: ...n this guide are limited to the tools needed for Math 1314 with Integrated Technology The calculator references are to a Texas Instruments TI 84 Plus graphing calculator The keystroke sequences should...

Page 2: ...rien Getting Orien Getting Oriented ted ted ted The face of the calculator has five distinct parts Display Screen The display screen will show all computations and functions that you enter and will di...

Page 3: ...ich will be discussed in detail in this guide These gray keys are labeled as follows Y WINDOW ZOOM TRACE and GRAPH There are blue titles above these labels STATPLOT TBLSET FORMAT CALC and TABLE Many o...

Page 4: ...s that will move the cursor up down left or right When looking at graphs the left right arrow keys will move the cursor to the left right on the graph and the up down arrow keys will toggle between fu...

Page 5: ...5 The black keys access the most commonly used functions and menus that will be needed in the course Commonly Used Functions...

Page 6: ...give the digits from 0 9 decimal point and the usual arithmetic operations At the bottom right is the ENTER key that you will use to tell the calculator to perform the operations or functions that yo...

Page 7: ...a different color and most keys have a green letter or punctuation mark above it When the function given in blue is needed press the 2nd key then the button that has the required function above it So...

Page 8: ...make the screen lighter press 2nd With weaker batteries it may be necessary to make the screen darker With new batteries it may be necessary to make the screen lighter Clear To clear the entire main...

Page 9: ...tored in the calculator can be archived To do this press 2nd and select 5 Press ENTER Now mark the program to archive Press PRGM and cursor down to the program to archive Press ENTER An asterisk will...

Page 10: ...10 To recall a number press 2nd STO ALPHA letter ENTER...

Page 11: ...he number and press 4 and then ENTER To find the square root of a number enter the function first Press 2nd 2 x then enter the number and close parentheses Then press ENTER To find any other root of a...

Page 12: ...aluate 2 2 2 3 4 11 3 4 2 3 Example Evaluate 2 3 4 4 3 2 5 7 2e Example Evaluate 2 2 5 3 7 4 7 12 Note the use of the key for the leading values in the numerator and the denominator rather than the su...

Page 13: ...res to evaluate 2 4 AB C D if 9 7 12 2 A B C D Press 9 STO ALPHA MATH ENTER Press 7 STO ALPHA APPS ENTER Press 12 STO ALPHA PRGM ENTER Press 2 STO ALPHA 1 x ENTER Now press 2nd 2 x ALPHA MATH ALPHA AP...

Page 14: ...es so enter 1 2 for 1 2 Use the operation symbols for addition subtraction multiplication and division that appear in the problem Use for a leading negative rather than subtraction To raise a variable...

Page 15: ...15 Example Enter 3 2 2 5 4 f x x x on the Y3 line on the Y menu First rewrite the function as 1 2 3 2 5 4 f x x x...

Page 16: ...and enter the desired increment An increment of one is often useful but at times a larger or smaller increment may work better To finish TABLE SETUP for an automatic table of values make sure the word...

Page 17: ...is not defined at a listed value for x In the screen shot displayed above the function entered in Y2 is not defined when x 3 The table currently only displays the y values associated with x values fr...

Page 18: ...and corresponding values for Y1 Y2 and Y3 will appear in those columns Example Use the functions that were entered in the Entering Functions in Y Entering Functions in Y Entering Functions in Y Enteri...

Page 19: ...will show up when graphing Of the three functions listed on the screen shot below only Y1 will appear on the graph since the other two functions have been disabled Press GRAPH to view the graph of the...

Page 20: ...e y minimum to get a better view of the function To find an appropriate Ymin value use trial and error or scroll down the TABLE to see the smallest y value in the list between x values of 2 and 7 The...

Page 21: ...ill display no tick marks Example Graph the function entered at Y2 First go to Y to turn off Y1 and turn on Y2 Press GRAPH The WINDOW is still set for the function entered at Y1 To return to the stand...

Page 22: ...the portion in quadrants 2 and 3 in greater detail change the window to 5 2 1 6 with scales of 1 on both axes To view the quadrant 4 portion in greater detail change the window to 0 12 12 4 with scal...

Page 23: ...ns in Y1 and Y2 and enable Y3 Then press GRAPH The modified window was still in place so the display shows no part of the graph of the function entered in Y3 Revert to the standard viewing window by p...

Page 24: ...n Example Enter the function 3 2 2 3 5 9 3 4 f x x x x on the interval 1 5 Put parentheses around the function when entering it into Y Then press the division key to separate the function from the dom...

Page 25: ...Enter the function as follows Y 2 X 3 X 2nd MATH 6 1 X 2 x 2 X 2nd MATH 3 1 The graph of the function will look like this An alternate means of entering a piecewise defined function on a TI84 calculat...

Page 26: ...generates the same graph Some older TI calculators can require different operation symbols for graphing piecewise defined functions If the multiplication symbol between the function and its domain doe...

Page 27: ...be made to the graphing window Graph a function by entering the function in Y The graph shown is Y1 as entered in the earlier examples When TRACE is activated the calculator places a cursor on the scr...

Page 28: ...view Press ZOOM 1 ENTER Then move the cursor above and to the left of the region to expand Press ENTER Use the right arrow key to move as far to the right as desired then use the down arrow key to mo...

Page 29: ...M 5 generates a square viewing window Since the display screen is wider that it is high the standard viewing window is slightly skewed This view adjusts the dimensions so that each tick on the x axis...

Page 30: ...provides a means for finding the local or relative maxima of a function intersect provides a means for finding any points of intersection when two or more functions are graphed value Enter a function...

Page 31: ...ht Bound Use the right arrow key to move the cursor so that it is to the right of the zero Press ENTER The calculator asks Guess Press ENTER The location of the zero will appear at the bottom of the s...

Page 32: ...ght of the zero Press ENTER Note the arrowhead pointing left The two arrowheads are setting the interval within which the calculator will search for the zero Notice that the first point had a negative...

Page 33: ...zero Move the cursor so that it is to the left of the zero The location of the zero means the left bound needs to have a positive y value Press ENTER Now move the cursor to that it is to the right of...

Page 34: ...that it is to the left of the low point Press ENTER Move the cursor so that it is to the right of the low point Press ENTER Then press ENTER and read off the coordinates of the relative local minimum...

Page 35: ...e left of the low point Press ENTER Move the cursor so that it is to the right of the low point Press ENTER Note the two arrowheads at the top that are marking the interval within which the calculator...

Page 36: ...a relative local maximum is identical to the process for finding a relative local minimum Example Example Find the coordinates of the relative local minimum of the graph of 3 2 2 3 5 9 3 4 f x x x x E...

Page 37: ...the left of the high point Press ENTER Move the cursor so that it is to the right of the high point Note the two arrowheads at the top of the screen define an interval within which the calculator will...

Page 38: ...intersection before beginning the process If there are several equations entered in the calculator use the up and down arrow keys to toggle between the functions and press ENTER when the correct one...

Page 39: ...other function see the display at the top so press ENTER The calculator is waiting for verification Press ENTER The point of intersection is displayed at the bottom of the screen Example Find the poin...

Page 40: ...the leftmost point of intersection Press 2nd TRACE and select intersect Press ENTER Move the cursor so that it is close to the Quadrant 3 point of intersection Press ENTER The cursor will move to the...

Page 41: ...ion is shown at the bottom of the screen Next find the intersection point that appears to be near x 1 Press 2nd TRACE and select intersect Move the cursor close to x 1 Press ENTER The cursor will move...

Page 42: ...the second point of intersection are shown at the bottom of the screen Now repeat the process to find the third and final point of intersection Press 2nd TRACE and select intersect Move the cursor so...

Page 43: ...s ENTER Press ENTER The third point of intersection is given at the bottom of the screen Note There are two other features on the CALC menu dy dx and intf x dx Other features do the same operations an...

Page 44: ...he L1 column Enter the x coordinates of the data Put the cursor at the top of the L2 column Enter the y coordinates of the data There must be the same number of entries in both columns Example Enter t...

Page 45: ...le of values by typing 1 ENTER 2 ENTER 4 ENTER 6 ENTER 8 ENTER 9 ENTER Now move the cursor so that it is under the heading L2 Enter the y values from the table of values Before graphing verify that th...

Page 46: ...ered pairs come from L1 and L2 If the data are stored in different lists use the 2nd of the keys numbered 3 4 5 and or 6 to select the appropriate list s There are three choices for the mark a square...

Page 47: ...en Press Y Notice the references to Plot1 Plot2 and Plot3 at the very top of the screen To turn a STAT PLOT on or off use the arrow keys to move the cursor to the desired STAT PLOT Press ENTER In the...

Page 48: ...f TI graphing calculators other than the TI 84 it may be necessary to press STAT CALC LinReg ENTER ENTER to find a linear regression Note if 2 r is not displayed enable the Diagnostic feature of the c...

Page 49: ...es for a b and c are listed The value for 2 R is a measure of how well the quadratic regression model fits the data The closer it is to 1 the better the fit Rounding each of the values to four decimal...

Page 50: ...st find the regression coefficients and make sure that that information is the current information on the main screen Then press Y VARS Statistics EQ RegEQ on the succeeding menus Then press GRAPH to...

Page 51: ...51 If the STATPLOT is turned on the calculator will display both the scatterplot and the linear regression model...

Page 52: ...r the function in Y as Y1 Then return to the main screen Press MATH 8 VARS Y VARS FUNCTION Y1 comma X A Close parentheses and press ENTER Example Find 2 f if 2 3 7 4 f x x x Enter function MATH 8 VARS...

Page 53: ...ive enable both on the Y menu and press GRAPH To display only the derivative make sure it is the only function enabled on the Y menu Example Display the graphs of both 3 2 2 3 5 9 3 4 f x x x x and it...

Page 54: ...a STO ALPHA A Compute x and store it as W Press the number then STO ALPHA W Press Y and enter the following commands as Y5 sum seq Y1 A K W W K 0 N 1 Press VARS Y VARS Function 5 ENTER Example Use a...

Page 55: ...Y1 Enter the number or rectangles n as N so press n STO ALPHA N Enter the left endpoint of the interval a as A so press a STO ALPHA A Compute x and store it as W Press the number then STO ALPHA W Pre...

Page 56: ...56 Result Choose sum Result Press 2nd STAT and Result Press seq choose OPS Result Result Press VARS Y VARS Enter Y1 A K W W K 1 N Function Y6 ENTER Use Alpha keys for letters...

Page 57: ...a b on a b Enter the integrand at Y as Y1 Then press MATH 9 VARS Y VARS Function Y1 comma X comma A comma B Example Evaluate 3 3 2 1 3 5 7 x x dx Enter 3 2 3 5 7 x x at Y as Y1 Press MATH 9 VARS Y VAR...

Page 58: ...program into the calculator using the Alpha keys for letters and operation keys for symbols Press ENTER at the end of each line you type Many of the commands needed in programming are accessible on th...

Page 59: ...This screen verifies the request Press ENTER Now answer the prompts In this Riemann sum problem the calculator wants a value for A Enter 2 Now enter a value for B Enter 10 Next enter the number of rec...

Page 60: ...60 Next decide between left endpoints right endpoints and midpoints Enter 0 for left endpoints Press ENTER...