Graphing Functions: TI82

• The steps for graphing a function are as follows:
  
  
  1. Entering the function: [Y=] menu
     
     
  2. Setting the WINDOW: [WINDOW] menu
     
     
  3. Viewing the graph: [GRAPH]
     
     
  4. Manipulating the graph: [TRACE] and [ZOOM]
     
     
  
  
• Example:  Graph y = x² - 3 x + 2 for values of x in the interval [-3, 3].  Find the approximate value of x that corresponds to y = 5, with the restriction that x lies in this interval.
  
  
  1. Enter the Function
     
     
     1. Clearing functions from the [Y=] window:
        
        Press [Y=].  If there are functions on any of the lines Y₁=, Y₂=, ..., then clear them by moving the cursor to each such line and pressing [CLEAR].  Exit this window by pressing [QUIT] (which is [2nd][MODE]).
        
        
     2. Turning Plots Off:
        
        Go to the [STAT PLOT] menu (press [2nd][Y=]).  There you can see whether or not a Plot is turned On.  To turn a given Plot Off, move the cursor down the list to the designated Plot and press [ENTER].  In this new screen, move the cursor to Off and press [ENTER].
        
        
     3. Now return to [Y=] and type in the function on the Y₁= line.
        
        
  2. Set the WINDOW
     
     
     1. The [WINDOW] parameters include Xmin, Xmax, Ymin, and Ymax.  These values determine the x- and y-dimensions of the graphics screen.  The other parameters, Xscl and Yscl, determine the spacing of tick marks on the x- and y-axes.
        
        
     2. In determining values for the Ymin and Ymax parameters, [TABLE] (which is [2nd][GRAPH]) can be useful.
        
        
        1. First go to [TBLSET] (which is [2nd][WINDOW]), and make sure that Indpnt: is set to Ask and Depend: is set to Auto.
           
           
        2. Then go to [TABLE].  You can enter any x-values you want and the corresponding y-values will be displayed in the Y₁ column.
           
           
     3. Return to [WINDOW] and set the [WINDOW] parameters as shown.
        
        Obviously, we want Xmin=-3 and Xmax=3.  By trial and error we see that y must be in the interval [-1, 20] whenever x is in the interval [-3, 3].  So we take Ymin=-1 and Ymax=20.
        
        
  3. Graph the function
     
     Now you should be able to obtain a graph of your function by pressing [GRAPH].
     
     
  4. Manipulate the graph.
     
     
     1. At this point you are in the [GRAPH] screen.  Press [TRACE] to activate a tracer on the graph itself.  You can find the location (the x- and y-coordinates) of the tracing cursor at the bottom of the screen.  Use left- and right-arrow keys to move the cursor until its y-coordinate is as close to 5 as possible.  You won't hit it exactly, but you can tell that x must be between -.82 and -.76.
        
        
     2. You can get a more accurate estimate by getting a closer look.  Press [ZOOM], move the cursor to the option 2:Zoom In, and press [ENTER].  Press [ENTER] once again, and you will see a magnified section of the graph near the position of the tracing cursor.  Press [TRACE] again, and you will be able to get an approximation of the y-coordinate that is much closer to 5 than it was before (with x between -.797 and -.782).
        
        
     3. Be aware that, in utilizing the [ZOOM] command, the calculator will have changed the values of your [WINDOW].
        
        
     4. You can also get a more accurate estimate of the value of x that corresponds to y = 5 by going back to the [TABLE] screen and performing some trial and error with different values of x.
        
        

---

Last modified: Sat Sep 08 2001