Texas Instruments TI-82 Manual page 12

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G T G : TI-82
RAPHING ECHNOLOGY UIDE
arrow key to move the cursor vertically to the graph of y = –.25x. Now the numeral 2 is displayed in the top right
corner of the window. Next press the right and left arrow keys to trace along the graph of y = –.25x. When more than
one function is plotted, you can move the trace cursor vertically from one graph to another in this way.
Technology Tip: By the way, trace along the graph of y = –.25x and press and hold either ◄ or ►. Eventually you
will reach the left or right edge of the window. Keep pressing the arrow key and the TI-82 will allow you to continue
the trace by panning the viewing rectangle. Check the WINDOW screen to see that Xmin and Xmax are
automatically updated.
The TI-82's display has 95 horizontal columns of pixels and 63 vertical rows. So when you trace a curve across a
graph window, you are actually moving from Xmin to Xmax in 94 equal jumps, each called ∆x. You would
−
xMax xMin
calculate the size of each jump to be ∆x = . Sometimes you may want the jumps to be friendly numbers
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like .1 or .25 so that, when you trace along the curve, the x-coordinates will be incremented by such a convenient
amount. Just set your viewing rectangle for a particular increment ∆x by making Xmax = Xmin + 94·∆x. For
example, if you want Xmin = -5 and ∆x = .3, set Xmax = -5 + 94 · .3 = 23.2. Likewise, set Ymax = Ymin + 62 · ∆y
if you want the vertical increment to be some special ∆y.
To center your window around a particular point, say (h, k), and also have a certain ∆x, set Xmin = h – 47 · ∆x and
Xmax = h + 47 · ∆x. Likewise, make Ymin = k – 31 · ∆y and Ymax = k + 31 · ∆y. For example, to center a window
around the origin, (0, 0), with both horizontal and vertical increments of .25, set the range so that Xmin = 0 – 47 ·
.25 = –11.75, Xmax = 0 + 47 · .25 = 11.75, Ymin = 0 – 31 · .25 = –7.75, and Ymax = 0 + 31 · .25 = 7.75.
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See the benefit by first plotting y = x + 2x + 1 in a standard graphing window. Trace near its y-intercept, which is
(0, 1), and move towards its x-intercept, which is (–1, 0). Then press ZOOM 4 and trace again near the intercepts.
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2.2.6 ZOOM: Plot again the two graphs, for y = –x + 4x and for y = –.25x. There appears to be an intersection near
x = 2. The TI-82 provides several ways to enlarge the view around this point. You can change the viewing rectangle
directly by pressing WINDOW and editing the values of Xmin, Xmax, Ymin, and Ymax. Figure 2.33 shows a new
viewing rectangle for the range displayed in Figure 2.32. The cursor has been moved near the point of intersection;
move your cursor closer to get the best approximation possible for the coordinates of the intersection.
Figure 2.32: New WINDOW Figure 2.33: Closer view
A more efficient method for enlarging the view is to draw a new viewing rectangle with the cursor. Start again with
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+ 4x and y = –.25x in a standard viewing rectangle (press ZOOM 6 for the
a graph of the two functions y = –x
standard window, from –10 to 10 along both axes).
Now imagine a small rectangular box around the intersection point, near x = 2. Press ZOOM 1 (Figure 2.34) to draw
a box to define this new viewing rectangle. Use the arrow keys to move the cursor, whose coordinates are displayed
at the bottom of the window, to one corner of the new viewing rectangle you imagine.
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