Table problem I try to build a table for X, Y1 and Y2 the table only displays X and Y1, not Y2. I can only highlight the y1 = sign or the Y2 = sign, but not both. any suggestion to correct this? thanks

This is problem with graphing differential equation. Invalid Axes error occurs if Axes=TIME or if t(time) is set as a CUSTOM axis. This is important to noticed: if Fields=DIRFLD you cannot plot a time axis. See captured image:




This graph represented differential system of equations y1'(x)=y2(x), y2'(x)=-y1(x) for initial conditions y1(0)=0, y2(0)=-1.Finally, x axes=y1(x) and y axes=y2(x)

The site seems to eat the plus signs I enter, so I will use PLUS to symbolize addition.

To find the equation of the straight line (y = a*x PLUS b) that passes through two points P1(x1,y1) and P(x2,y2) , you need to use
1. the coordinates of the points to calculate the slope a (gradient) as a=(y2-y1)/(x2-x1)
2. Replace the calculated value of a in the equation and write that one of the points ( P1(x1,y1) for example) satisfies the equation. In other words y1=a*x1 PLUS b.
Here y1 and x1 are known values, a has been calculated, and only b is still unknown. You can now use the equation y1=a*x1 PLUS b to calculate b as
b=(y1-a*x1)

Example: Equation of the line through (1,5) and (3,6)
Calculate the slope (gradient) of the line as a=(y2-y1)/(x2-x1) where y2=6, y1=5, x2=3, and x1=1. You should get a=(6-5)/(3-1)=1/2
The equation is y=(1/2)x PLUS b, where b is not known yet.

To find b, substitute the coordinates of one of the points in the equation. Let us do it for (3,6).

The point (3,6) lies on the line, so 6=(1/2)*3 PLUS b.
Solve for b: 6 MINUS 3/2=b, or b=9/2=4.5
Equation is thus y=(x/2) PLUS 9/2 =(x PLUS 9)/2

I trust you can substitute you own values for (x1,y1, x2,y2) to duplicate the calculations above.

At some time or other you executed the Transfrm Application. I remains in ram and takes over the graphing duties from the native OS. You must unload it from memory. Do not worry this will not delete it.
To unload it from RAM

1. Press the APPS button.
2. In the list of APPS look for Transfm. You will have to scroll down or Up (faster) to get to it.
3. Select it and press [ENTER]
4. A new screen is displayed inviting you to Uninstall or Continue.
5. Press the number key corresponding to Uninstall.

Return to the [Y=] function editor to type in the functions to graph. Make sure that the = signs after the Y1,Y2, are highlighted. If one of them is not highlighted, move cursor on = and press ENTER

Let us see if I understand what you want to do. You have two functions f and g. With f and g you create four functions,

1. f+g, which you want to evaluate at 0
2. f-g, which you want to evaluate at -1
3. f*g, which you want to evaluate at 1
4. and f/g, which you want to evaluate at 3

If that is not what you intend to do, then I am sorry to I that interpreted incorrectly and you will have to post a comment with more information.
If however I did understand what you want to do, then there is a simple way to achieve this

1. In the [Y=] function editor, enter Y1 and Y2
2. In your mind decide which one represents f(x) and which represents g(x), probably f(x)=Y1(x) and g(x)= Y2(x)
   
3. Validate each one by pressing [ENTER]
   
4. Do not worry about graphing the function.
5. Press [2nd][QUIT] to return to main calculator screen
6. Enter a value (for example 5) and store it in variable X; to do so you press 5 [STO->][X,T, theta,n] [ENTER]
7. To calculate f(x)+g(x) or (f+g)(x) on the command line in main calculator screen

• Press [VARS][=>][Y-VARS][1:Function][1:Y1][ENTER]. Main calculator screen echoes Y1
• Press [+]. Screen shows Y1+
  
• Press [VARS][=>][Y-VARS][1:Function][1:Y2][ENTER]. Main calculator screen echoes Y1+Y2
• Press [ENTER] to obtain the value of f+g at X=5
  

As you can see, if you want a different operation f-g, f*g, or f`/g for a different value of X, you will have to repeat steps 6 and 7.

I am going to show you how to create a small program that will perform all the 4 operations in sequence, each time asking you for the value of X you want to use. If you are not interested, you can ignore what follows. I remain convinced that it will be helpful for other visitors.

Creating a simple program

Press [PRGM]
Use arrow to highlight [NEW]
Press [ENTER]
Screen displays
PROGRAM
Name= with alpha cursor blinking
Type in the name, for example FOPG ( meaning F operation G) or anything else. Do not use a keyword (reserved command of the TI84Plus) These are what you find in the [CATALOG].



The top line on each screen capture is inserted by the program editor after you choose the name. The last line of first screen is the the same line as the second line on 2nd screen. It must not be entered. The colon : is supplied by the program editor. It is the beginning of an instruction.

There are only to commands that are repeated here: Disp and Prompt

Disp orders the program to display

1. a message (what is between the quotation marks) or
   
2. the result of a calculation: Y1+Y2, Y1-Y2, Y1*Y2, or Y1/Y2

Prompt X will display X=? and the blinking cursor. You are supposed to enter the desired value of X and press [ENTER].
The Disp and Prompt command are accessed through the command catalog by pressing [2nd][0] (CATALOG) then scrolling along the list of commands to find the one needed. Shortcuts are possible (see below)

How to key in the program steps within the program editor
: Disp "F+G"

Press [2nd][0] (CATALOG) [X^-1](D) [Scroll Down [till...] Disp
Press [ENTER]. Editor shows :Disp
Press [ALPHA] [+] ("). Editor shows :Disp "
Press [ALPHA][COS] (F). Editor shows :Disp "F
Press [+]. Editor shows :Disp "F+
Press [ALPHA][TAN] (G). Editor shows :Disp "F+G
Press [ALPHA][+] (") Editor shows :Disp "F+G"
Press [ENTER] to validate instruction
Calculator inserts a new line :

: Disp Y1+Y2
Press [2nd][0] (CATALOG) [X^-1](D) [Scroll Down [till...] Disp
Press [ENTER]. Editor shows :Disp
Press [VARS][=>][Y-VARS][1:Function][1:Y1][ENTER]. Editor shows :Disp Y1
Press [+] . Editor shows :Disp Y1+
Press [VARS][=>][Y-VARS][1:Function][1:Y2][ENTER]. Editor shows :Disp Y1+Y2
Press {ENTER] to validate instruction
Editor inserts a new line :


:Prompt X
Press [2nd][0] (CATALOG) [8](P) [Scroll Down [till...] Prompt
Press [ENTER]. Editor shows :Prompt
Press [X,T.theta,n] key. Editor shows :Prompt X
Press [ENTER] to validate instruction
Editor inserts a new line :

To save program
Once all instructions are entered, press [2nd][QUIT] to save program.

To run program

1. Press [PRGM]
2. Under the [EXEC] menu, the list of available programs appears.
3. Type the number corresponding to the one you want to run ( FOPG) and press [ENTER].
4. The main calculator screen displays prgmFOPG and blinking cursor.
5. Press [ENTER] to make it run
6. Enter a value of X and press [ENTER]
7. Follow instructions.

Hi,
In the Y= equation editor you can enter two functions, and graph them both or calculate a table for both. However, the two functions will be evaluated at the same values of X.

Rather than trying to guess what is happening, I will show you how to get your two tables.

If you have used one the applications Inequalz or Transform it si probably still stuck in memory, and you must unload it from the RAM before recovering the usual calculator behavio(u)r

1. Press the [APPS] button, find Inequalz or Transform, point to it and click [ENTER].
2. You will be asked to Continue or Quit the application.
3. Press the number corresponding to Quit (usually 2).
4. Press [2nd][Y=] (STAT PLOT). Press [4:PlotsOff][ENTER]
   
5. Calculator replies Done.

Open the [Y=] equation editor. Type in your equations. Press [ENTER] at the end of each equation. Verify that the [=] signs after Y1, and Y2 remain highlighted when cursor is moved away from them.
Press [2nd][GRAPH] (Table) to see your 2 tables y1 and y2 calculated at the same X.

Hope it helps.
Thank you for rating the solution.

Hello,
Sorry if you already know that, but I want to make sure we understand one another.

Say you want to graph the function Y1=2X+3.
You press [MODE] to make sure that the FUNC on 4th line is highlighted permanently. If it is you press [Y=]

On the first line where it says Y1= you enter 2*[X,T,Theta,n] +3.
The X is accessed with the key to the right of the [ALPHA] key.
As you key in your function, notice that the equal sign after Y1 is highlighted and remains so. When you finish entering the function press [ENTER] so that the cursor moves to the line Y2=. Make sure that the = sign after the Y1 in previous equation remains highlighted.

You can now draw the graph by pressing [GRAPH] or generate the table Y1=f(X) by pressing [2nd][TABLE]. Under no conditions should you enter YOUR own values. If the table does not appear there may be a problem, and you will not solve it by entering values.

Now let us try to get you calculator to work as it should.

Press [2nd][STATPLOT][4:PlotsOff] , the command PlotsOff echoes on main screen. Press [ENTER] to turn statistical plots OFF. Screen displays Done.
Press [2nd][CATALOG] [ENTER]. The list of all avilable command appears. Scroll down till you reach ClrAllLists. Move arrow to the correspondig line and press [ENTER] , command echoes on main screen as ClrAllLists. Press [ENTER] to erase all old statistical lists that may be stored in the calculator memory.

Now you are ready to graph or create the table of values. Press [2nd][Table] and the table should be displayed. All you can do with the values in the table is to look at them, examine them. You cannot modifie nor erase them.

If, for reasons of your own, you think you ought to be allowed to enter YOUR values, in the table, then this is not graphing functions. The name for that is DOING STATISTICS. And the procedure is tottaly different: You enter YOUR values in lists and use the calculator to draw the data points, and to find the best fit (the curve that models the pattern of data distribution best). When you decide which fit is the best, you can use the calculator to extract the equation for the curve and, if you want it, to draw the curve on the same graph where you raw data is represented.
Hope these clarifications helps.





Before jumpin

Hello,
Sure you can. Values of Y1 and Y2 will be calculated for the same value of the independent variable. here is a screen capture taken with NO special configuration. Functions represented are Y1=2X, Y2=4X.

If you have a
Hope it helps.

Hello,

Suppose you want to draw the circle the equation of which is X^2+Y^2=4, a circle centered at the origin with radius 2.
When you isolate Y^2 and then extarct the squre root you obtain two solutions, call them Y1 and Y2
Y1=SQRT(4-X^2), Y2= -SQRT(4-X^2)
You press[Y=] and type in the right hand side of the equations above, one in Y1= and the other in Y2. Press [GRAPH].

Ih a graphic does not appear within the scree window adjust the window parameters ( [WINDOW]) or Press [ZOOM] and select ZoomIn, ZoomOut, ZoomSTD, etc.

Explore the program Draw accessible by pressing [2nd][DRAW].

Hope it helps

Hello,
Here how you do it taking as exemples y1=x^3 -5 and y2=abs(x^3-5)
Turn calculator ON by pressing [AC/On] . Use arrows to select [Graph] icon and press [EXE]
On line Y1= enter X[^]3 -5 [EXE]
On line Y2= press [OPTN] [F5:NUM][F1:abs] [(] X [^]3 -5 [)] [EXE]
The graphs will be drawn one after the other. You might have to adjust the window limits.
Here is an ouput drawn on another calculator.

For negative values of the x-variable, Y1 has negative values, while in the same range, Y2 has positive values, equal and opposite to those of Y1. In that range, Y1 and Y2 are symetric of each other with respect to the X axis.
For positive values of the x-variable, Y1 and Y2 are identical.

Hope it helps

w2 and y2 are used for 2stage applications

w2 = 2 stage heat
y2= 2 stage cool

If your system is a single stage system, look for the y1 and y2 terminals. If the thermostat does not have y1 and y2 then you may have the wrong thermostat. As always, please read the directions carefully. Thanks!