Download TI-89/92 Plus Calculator: Math Functions, Evaluation, Plotting, and Equations and more Study notes Algebra in PDF only on Docsity!
MATH 105
TI-89/92 Plus Graphing Calculator Tasks
I. Graphing Functions
Enter the function into the calculator. Press! ".
Type in the function and press!#. For the independent variable, use x.
This can also be done from the home screen using $ 1:Define and then typing y1(x)=and the function definition. Press #.
Graph the function. To graph and make sure your graphing screen displays the “standard window,” in which x and y both range from -10 to 10 , press % Zoom and then 6:ZoomStd. If you just press !&, the function will appear in the last window the calculator used.
If you do not see the graph, or you only see part of it, press! ' and choose a different window size.
II. Special Functions
Absolute Value function , x. Press! " then type abs(x) for the absolute value of x. Alternately, press! " then () and choose 1:Number and then 2:abs(. Type in what goes inside the absolute value symbols and don’t forget to close the parentheses.
Greatest Integer function (step function) Press! " then type int(x) for the greatest integer function of x. Alternately, press! " then () and choose 1:Number and then 4:iPart(. Type in what goes inside and don’t forget to close the parentheses.
Piecewise Defined Functions This is best explained by an example. To enter
y = , do the following.
3 x − 1, x < 1 2 x + 5, x! 1
! " then type into y1 the function !"#$ (* (This is above the K key, the symbol is called “when.”) and then (^) " ( + $. For (^) y2 type %"&' (* (,- $. Press! & to see the graph.
III. Evaluating Functions
If you have a function f ( x ) and wish to evaluate the function for certain values of x , you can enter the function into your calculator and have it evaluate for you.
From the home screen press $ 1:Define and then type f(x)=and the function definition. Press (^) #. Next type (^) f(5) (or whatever value for (^) x you want) and press (^) #.
If you wish to evaluate the function at many different values, you can use a TABLE.
Enter the function into y1. Press! ..
Use / to change the settings. tblStart is the first value for x that you wish to display; „tbl is the increment for x (so if tblStart is 0 and(„Tbl = 0.5 the x values will be 0, .5, 1, 1.5, etc.); if you choose AUTO, the table will be generated automatically; if you choose ASK, the calculator will ask you to type in the x value. Press # to save this information. Once you are done setting up the table, press!
IV. Plotting Points and Finding Regression Curves
1. Enter your data values. Press! 3 to make sure you are on the main screen. Press 4 and choose 6:Data/Matrix Editor. Next choose 3:New.
Make sure Type is set to Data and Folder is set to main. In the Variable box type a variable name, for example stat, and press #. Press # again and you see the Data Editor.
Enter the values of the independent variable in (^) c and the values of the dependent variable in c2.
The next time you wish to enter data, you can press 4 , then 6:Data/Matrix Editor, and then 1:Current. Then simply clear the old lists and put in new ones.
For Calculation Type press 06 and choose 5:LinReg.
In the x box enter c1 and in the y box enter c2. Move down to Store RegEQ to and press 6 and then select y1(x) and press #. Press # again to see the regression line. The equation of the regression line is stored in the " editor as y1.
Press # to clear this screen.
4. Plot the regression line through the points.
Press! &.
5. Return your calculator back to normal graph mode. To turn off the scatter plot, press! " and highlight Plot 1. Press $ to deselect Plot 1 and then press % Zoom and choose option 6:ZoomStd. 6. Predict some values using the regression line. Make sure the values you want to plug in for x are between the highest and lowest x values of your data (do not extrapolate). Press! 3 to return to the home screen. In the command line type y1(#) where # is the input value you want to use and press #.
V. Solving Equations/Finding Zeros of Functions
If you have an equation to solve, press! 3 to make sure you are on the home screen and then press % and then 1:solve. Type in the equation you wish to solve, followed by the variable you wish to solve for, for example solve(x:2-2x=15,x). Don’t forget to close the parentheses. Press #.
VI. Finding Points of Intersection of Curves
If you want to find where the graphs of f ( x ) and g ( x ) meet, solve the eqution f ( x ) = g ( x ) as above. This will give you the x coordinate of the point where they meet. Don’t forget to find the y coordinate.
VII. Finding Maxima and Minima
This also relates to finding where a function is increasing and where it is decreasing, because the locations of the maxima/minima are the places where the function changes from increasing to decreasing or vice versa. This is also useful in finding the range of a function.
If you have a function f ( x ), press! "and then type in the function f ( x ) and press #. Graph the function by pressing! & and make sure the maximum/minimum you want to find is in the viewing window. Now press 9 and choose option 3:Minimum or 4:Maximum.
The calculator will ask you to move the cursor to find a lower bound to where the maximum/minimum is. Use / to move to the left of where the maximum/minimum is. Press ".
You are now asked to move the cursor to find an upper bound to where the maximum/minimum is. Use / to move to the right of where the maximum/minimum is. Press " and the calculator will locate the maximum/minimum
In both of these, instead of using / to get to the left and right of the maximum/minimum, you can save time by simply typing in a number. For example, when you are asked for a lower bound in the above example, just press the ; and 1 keys and then ", since -1 is to the left of the maximum/minimum we are looking for. Occasionally you may get an answer such as -1.49999995. You can be reasonably certain the answer is -1.5. Also, keep in mind that a calculator answer of 2.3333333 is really 2 13 or 83 .If you get a decimal answer for which you do not recognize the rational number equivalent, make sure your instructor allows an approximate answer for the problem. If not, you will need to find the exact answer using algebra.
Also, make sure you look at the graph in a larger and/or smaller window. Doing this will ensure that you see all of the maxima/minima. You will need to find them all.
