Functions
This section is currently under construction.
1. How do I set up a function in the TI83?
Answer:
Step 1. Press the [Y=] key to open the function editor.
Step 2. Type in the function you want in the Y1= line.
Step 3. Press [2nd] [QUIT].
2. How do I create a table of numbers using the Y1 function?
Answer:
Step 1. Press [2nd] [TBLSET] to open the table setup menu. On the line "Indpnt", highlight "Ask" and press enter. On the line "Depend", highlight "Auto" and press enter.
Step 2. Now press [2nd] [TABLE] , type in a value for "X", and press [ENTER].
Step 3. Continue typing more values for X to fill up the table.
3. How can I see more decimal places for the numbers in a table?
Answer:
Step 1. Use the arrow keys to move the highlight over the number you are interested in seeing to more decimal places.
Step 2. Read the number at the bottom of the screen. You should be able to see anywhere from 9 to 14 significant figures for your number.
4. How can I delete the numbers in a table?
Answer:
The following procedure will work when the table setup has been set to ask for the values of the independent variable.
Step 1. In the table screen, check the bottom of the screen to make sure that the cursor is not blinking at the bottom of the screen. If the cursor is blinking, press the [ENTER] key to stop the cursor from blinking.
Step 2. Use the arrow keys to move the highlight to the first number in the first column of the table (the "X" column).
Step 3. Press and hold the [DEL] key to delete the numbers in the first column of the table. The entire table should become clear with this procedure.
5. How can I set up the cube root function in the Y= menu or on the home screen?
Answer #1: Type [MATH] [4] followed by [X] [ ) ].
Answer #2: Type [3] [MATH] [5] [X].
Answer #3: Type X^(1/3).
6. How can I graph a function that is in the Y1 function variable?
Answer :
Step 1. Go to the Y= editor and make sure that the = sign for the function is highlighted.
Step 2. Press [ZOOM] [6]. This will plot the function in the standard window.
Note: In the Y= editor, do not highlight Plot1 or Plot2 or Plot3 unless you want a statistical plot together with your function graph. If Plot1, Plot2, or Plot3 is highlighted, put the cursor over the highlights one by one and press [ENTER] to remove the highlights. Then do step 2 above.
7. How can I set up a piecewise function?
Answer :
The idea is to use the TEST functions as found in the [2nd][TEST] menu. These functions have values which are 0 or 1 depending if the "condition" is satisfied. In the following examples, we will use the symbol >= to mean "greater than or equal to", and <= to mean "less than or equal to". When entering a function into the calculator, the more standard symbols as found in the TEST menu should be used.Here are some examples:
Example #1: Suppose f(X) = X/2 if X is >= 0, and f(X) = 1 - X if x is < 0. Then enter (X/2)(X >=0) + (1-X)(X < 0) .
Example #2. Suppose f(X) is X/2 if X is >= 0, and undefined otherwise. Then enter (X/2) / (X >= 0).
Example #3. Suppose f(X) is X/2 if X is in [0 , 3], and zero otherwise. Then enter (X/2)(X >= 0)(X <= 3).
8. When I try to graph I get error "dimension". What does this mean?
Answer:
You probably have the stat plots on. Press the [Y=] button. When you get the screen for that, look at the top. You will see the words Plot 1 Plot 2 Plot 3. If any of these are highlighted, they must be disabled. Move the cursor to a highlighted Plot and then press enter. This should remove the highlight. Do this for each highlighted plot. When all plots have been disabled try graphing again.
9. How can I graph a family of curves, such as x2 + 3 y2 = C, for C = 1,4,9 ?
Answer:
Here is one possible solution. In the Y= menu, set Y1 equal to (({1,4,9} - X*X)/3)^(1/2), the upper half of the ellipses.Then set Y2 equal to - (({1,4,9} - X*X)/3)^(1/2), the lower half of the ellipses. Then press [ZOOM] [4] (the decimal zoom). The three ellipses will appear in the graph window.
10. How can I set up a table of function values on the TI85 calculator?
Answer:
The TI85 does not have a table window that is similar to the one on the TI83. However, one can obtain a list of function values on the TI85 as follows: Set up the function y1 in the usual way on the TI85. Then create a list of values (using the {...} keys), and store the list in the variable x. Then enter y1 on the home screen. The function values will appear as a list on the home screen. For example, if {1,2,3} is stored in x, and if y1 is the function x*x, then the output after entering y1 on the home screen is {1,4,9}.
11. When I plot the function (X^2) * Cos(20 Pi X) in the decimal window, why do I get a parabola?
Answer: In the decimal window, the distance between pixel points in the X-direction is .1 . Thus, the change in 20 Pi X from one pixel point to the next is 2 Pi. Also, X = 0 is a pixel value. Thus, 20 Pi X evaluates to a multiple of 2 Pi at any pixel point. Thus, Cos(20 Pi X) evaluates to one at any pixel point. That leaves us with the X^2 term, so the graph is of the function X^2, a parabola.
12. Can you give me some pointers on how to set up a good window to view a graph?
Answer: There is no easy answer to this. If you are interested in the graph for specific values of x, say -3<x<3, you can key in xmin=-3 xmax=3 in the appropriate places after pressing [WINDOW]. Then you can do a ZOOM 0. The problem is that the y values may be so big that some of the essential features of the graph are lost. So there really is no answer to this except that if you can get the appropriate information about the shape of the graph from calculus, that is the way to go.
13. How can I find the solution to the equation f(X) = 0 ?
Answer #1: First plot the function in such a way that the crossing of the graph with the X-axis is clearly visible. In the graph window, press [2nd] [CALC] [2], the "zero" operation. This will bring you back to the graph window, where the question "Left Bound?" will appear. Use the left and right arrow keys to position the cursor on a graph point to the left of the zero. Press [ENTER]. Now a second question "Right Bound?" will appear. Use the arrow keys again to position the cursor on a graph point to the right of the zero. Press [ENTER]. Now a third question "Guess?" appears. Move the cursor near the zero (but inside the left and right bounds) and press [ENTER]. The calculator will calculate an accurate value of the zero and display the result at the bottom of the graph window. This value is also left in the variable X.
Answer#2: We will assume that the function is located in the Y1 variable. On the home screen, press[2nd] followed by [CATALOG]. Scroll down to the "solve(" function and press [ENTER]. This will bring you back to the home screen. Complete the "solve" function by typing Y1,X, guess) , so that the completed instruction is of the form solve(Y1,X,guess). (Note that "guess" is a number which is near to the zero of f(X).) Now press [ENTER]. The calculator will compute the solution to f(X) = 0 and display the result. Note that the calculator will not store this result in the variable X unless you next type [STO->] [X] [ENTER].
14. In order to zoom in on a graph, I moved the graph cursor to a point near my function graph. I then zoomed in, and the graph disappeared completely. What happened?
Answer: Chances are good that your zoom factors are too large. You should go to the ZOOM FACTORS menu ( [ZOOM] , [right arrow] , [4] ) and reduce the zoom factors.
15. How can I zoom in on a graph of a function?
Answer: Press [ZOOM] , [2] . The calculator will display your graph with a blinking cursor. Use the arrow keys to move the cursor near a point of the graph. Then press [ENTER]. The calculator will zoom in to the "zoom point", which becomes the new center of the graph, and replots the graph of the function. The window variables are all updated.
16. How can I compute a) cot -1(x) , b) sec -1(x) , and c) csc -1(x) using the TI-83 calculator?
Answer:
Part a) There are various identities that one can use for cot -1(x). In particular, cot -1(x) = Pi/2 - tan -1(x), which is valid for all x. Also, cot -1(x) = tan -1(1/x) if x > 0, and cot -1(x) = Pi + tan -1(1/x) if x < 0.
Part b) There are various identities that one can use for sec -1(x). The identities depend on how one defines sec -1(x). With the usual definitions, we have sec -1(x) = cos -1(1/x) for x > 0. For x < 0, some definitions will give sec -1(x) = 2(Pi) - cos -1(1/x) . Other definitions will give sec -1(x) = cos -1(1/x) . Thus, for x < 0 , you need to check your textbook to see which definition of sec -1(x) you are using, in order to determine which identity to use.
Part c) Similarly, there are various identities that one can use for csc -1(x). Again, the identities depend on how one defines csc -1(x). With the usual definitions, we have csc -1(x) = sin -1(1/x) for x > 0. For x < 0, some definitions will give csc -1(x) = Pi - sin -1(1/x) . Other definitions will give csc -1(x) = sin -1(1/x) . Thus, for x < 0 , you need to check your textbook to see which definition of csc -1(x) you are using, in order to determine which identity to use.
Related questions
Q1. When I plot the graph of tan(x) in the standard window, why does no graph appear?
Q2. How do I enter the variable Y1 onto the home screen?
Q3. How can I find the coordinates of inflection points with the calculator? I try tracing but don't really know if I am on or near the inflection point.
Q4. I try graphing y=(x^2-1)/(x-1) . The teacher says I should get something that looks like a line but I don't. What am I doing wrong?
Q5. How do I stop the machine from graphing while it is graphing?
Q6. How do I graph a function of y?
Q7. My screen shows that my two graphs intersect in two points, but each time I try to calculate the intersection, I always get the first intersection point. Why can't I get the second intersection point?
Q8. How do I find the intersection of curves when the graphs are done in parametric mode?
Q9. I am in the standard window and want to get the cursor to the point on the curve where x=9. So I press trace and then the right arrow button a million times. Isn't there a faster way to get there?
Q10. I entered the expression (X^2)*(Y^3) into the Y1 function variable. I then went to the home screen and stored the number 2 into Y. Next, I pressed [GRAPH], expecting to get the graph of 8*(X^2). Instead, I got the message "ERROR: INVALID". What happened?
Q11. How can I plot the graphs of y=f(x), y=f -1(x), and y=x on the same set of axes?
Q12. How can I transmit information from one TI-83 calculator to another TI-83 calculator using the "communication link"?
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Frequently Asked Questions
Basics of Calculator Operation
Functions
Limits
Derivatives
Curve Sketching
Integration
Inverse Functions
Parametric Equations
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Vectors and Matrices
Functions of Several Variables
Multiple Integrals
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