On the Main Menu of the calculator, we select 5, GRAPH (the Graph Function Menu).

We will graph

Enter the function we are going to graph in Y1=, then hit the blue EXE key

To actually enter the viewing window, select the yellow SHIFT followed by F=3(V-Window).

Now, we will enter the viewing window in two steps.

1)  We will enter the domain by noticing the x-intercepts.  Clearly, if we set each factor equal to zero and solve, we get three   x-intercepts, x = 0, x = 30 and x = 50.  So, let’s graph on a window that is slightly left of x = 0, and slightly right of x = 50.  Set Xmin = -10, and Xmax = 60.  We will count by tens.    

So, enter SHIFT followed by QUIT.

Then F6(DRAW) to graph the window you now have.  Note the Ymin and Ymax, are still set to -10, and 10 respectively.  The resulting graph is neither complete or representative of the global view.  Simply put, just three faint branches appear.  And since we’re graphing a polynomial function, we know the graph should be continuous. 

2)  So, this is all OK. Because now we will allow the calculator to calculate an appropriate range. 

By entering F2(Zoom) and then selecting F5(AUTO), the calculator will compute an appropriate range for the domain you entered.  That is, the calculator will find Ymin and Ymax to fit the domain you entered.  NOTE:  The domain must be entered first to use the ZOOM – AUTO feature.

Clearly we can now see the complete graph.  Glance back at the viewing window. SHIFT, V-Window and observe the range values…. . 

On the Main Menu of the calculator, we select 5, GRAPH (the Graph Function Menu).

We will graph

Enter the function we are going to graph in Y1=, then hit the blue EXE key

Notice, the function does not appear in the display in it’s entirety.  

To actually enter the viewing window, select the yellow SHIFT followed by F=3(V-Window).

In the first example, we noticed factors, so we began by entering domain values in the viewing window.  Now, we notice the large constant on the end of the function, so unlike the example before, we will first begin by entering the range values. 

Let’s keep Xmin = -10, and Xmax = 10, but we will adjust the range values to include the y-intercept, which is (0,100).

So, we will straddle y = 100 and thus enter range values of Ymin = 0  and Ymax = 200.  To simplify life, we’ll count by tens. 

Now, let’s explore the graph of the function.  So, enter SHIFT followed by QUIT.  Then F6(DRAW) to graph the window you now have.

Notice, it appears from a distance your choice of domain values were both ‘good’ and ‘bad’.  ‘Good’ because that graph contains the end behavior that is typical for cubic polynomials.  But, if you examine the graph closely you see what may resemble a faint horizontal linear portion to the graph.  Since this is a cubic, you know the graph must have curvature to it.  So, this leads us the ‘bad’.   We need to zoom in on the portion of the graph that has this faint misleading linear portion to explore it more closely. 

So, approximate both the x and y values that could serve as a boundary for this faint linear portion. 

Enter these approximate domain and range values in the viewing window. 

Now graph what you just entered. 

Clearly we need to continue to zoom until we see the classical cubic shape. 

We’re playing what is kinda like math’s version of Hide-n-Seek. Find the cubic shape … .

To help us zoom, let’s see if the graph has a local max or min value.  To explore this, enter SHIFT, F5(G-Solv).  Then select either F2(MAX) or F3(MIN). 

I selected F2 and found my graph had a local maximum value.

This gives me an idea as to how to revise my window as I continue this “zooming” process.  Let’s zoom further, allowing the x vales to not deviate too far from 0.090 and the y values to not deviate too far from 100.003. 

With successive zooming, we finally settle on a viewing window, as indicated above.  

Once graphed on this window, we can clearly now see the complete graph, the classic cubic shape clearly resonates with it’s unmistakable end behavior.