Texas Instruments TI-82 Manual page 9

Figure 2.20: Connected graph of y = [[x]]
The true graph of the greatest integer function is a step graph, like the one in Figure 2.21. For the graph of y = [[x]],
a segment should not be drawn between every pair of successive points. You can change from Connected line to
Dot graph on the TI-82 by opening the MODE menu. Move the cursor down to the fifth line; select whichever graph
type you require; press ENTER to put it into effect and GRAPH to see the result.
You should also change to Dot graph when plotting a piecewise-defined function. For example, to plot the graph of
 + <
2
x 1, x 0
f (x) = , enter the expression (x

− ≥
x 1, x 0

2
x + 1) ( 2nd TEST 5 0 ) + (
(
X,T,θ X,T,θ
and press GRAPH.
2.2.4 Graphing a Circle: Here is a useful technique for graphs that are not functions, but that can be "split" into a
top part and a bottom part, or into multiple parts. Suppose you wish to graph the circle whose equation is x
36. First solve for y and get an equation for the top semicircle, y =
− −
2
36 x . Then graph the two semicircles simultaneously.
The keystrokes to draw this circle's graph follow. Enter
pressing Y= CLEAR 2nd
to draw them both.
Figure 2.22: Two semicircles
If your range were set to the standard viewing rectangle, your graph would look like Figure 2.23. Now this does not
look like a circle, because the units along the axes are not the same. This is where the square viewing rectangle is
important. Press ZOOM 5 and see a graph that appears more circular.
9
G T
RAPHING ECHNOLOGY
2
+ 1)(x < 0) + (x – 1)(x ≥ 0) somewhere in your Y= list by pressing
– 1 ) (
X,T,θ X,T,θ
2
( 36 – x ) ENTER CLEAR (-) 2nd
X,T,θ
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G : TI-82
UIDE
Figure 2.21: Dot graph of y = [[x]]
2nd TEST 4 0 ). Then change the mode to Dot graph
− 2
36 x , and for the bottom semicircle, y =
− − −
2 as Y
36 x and 36 x
1
( 36 –
X,T,θ
Figure 2.23: Circle's graph - standard view
2 2
+ y =
2 as Y
(see Figure 2.22) by
2
2
x ). Then press GRAPH