1. How do I graph y = x3 - 8x + 5?
Press Y= to open the graph editor, and then press CLEAR
to erase any previous function assigned to Y1. Now enter the expression
x3 - 8x + 5, press ZOOM , select
ZSTANDARD, and press ENTER .
Notice how an important part of our graph disappears off the top of our
screen. In this instance, we say that we do not have a "complete graph".
A complete graph should show all important features of a graph such as "turning
points" and "x & y intercepts". To get a better graph, try
pressing ZOOM , selecting ZOOM OUT, and then pressing ENTER
.
We can now see all the turning points in the graph, but the graph is also harder to read. Hence, let's go back to our original graph by pressing ZOOM , selecting ZOOM IN, and then pressing ENTER . We will now try to improve our graph by a different method. Press WINDOW and you will see a list of maximum and minimum values for x & y. These values determine the size of our graph window. Use the arrow keys to scroll down to YMAX, and change the value of YMAX to 15. Now press GRAPH and the resulting graph of Y1 will be complete.
2. How do I graph y = (1/2)x + 8?
Press Y= to open the graph editor, and then press CLEAR to erase any previous function assigned to Y1. Now enter the expression (1/2)x + 8, press ZOOM , select ZSTANDARD, and press ENTER .
Once again the graph is incomplete since we can't see where it crosses the
x-axis (the x intercept). To correct this, press WINDOW and use the
arrow keys to scroll down to XMIN, and change the value of XMIN
to -20. Now press GRAPH and you will now have a complete graph.
3. How do I graph y = 
?
Press Y= to open the graph editor, and then press CLEAR to erase any previous function assigned to Y1. Now enter the expression (x2 - x)/(x - 1), press ZOOM , select ZSTANDARD, and press ENTER . The graph looks pretty good, but the one important feature that is missing is the "hole" that should occur at x =1. The reason this happens is because a calculator graphs a function exactly as you do. It picks a finite number of points off of the x-axis, finds the corresponding y values, plots the points, and then connects the dots. Hence, if x = 1 is not one of the values chosen off of the x-axis, then the graph won't reveal that the function is undefined at x = 1.
To get a more correct graph, press ZOOM , select ZDECIMAL,
and press ENTER . This forces the graph to use the values 0, 0.1,
0.2, . . . off of the x-axis to generate points to plot, and when the calculator
reaches the value x = 1, it will correctly show the gap in the graph.
