17
G
RAPHING
T
ECHNOLOGY
G
UIDE
: TI-82
Copyright © Houghton Mifflin Company. All rights reserved.
Figure 2.49: Solving a system of equations
2.3.4 Solving Inequalities by Graphing: Consider the inequality
3
14
2
x
x−≥−. To solve it with your TI-82, graph
the two functions
3
1
2
x
y
=−
and y = x – 4 (Figure 2.50). First locate their point of intersection, at x = 2. The
inequality is true when the graph of
3
1
2
x
y
=−
lies above the graph of y = x – 4, and that occurs when x < 2 . So the
solution is the half-line 2x ≤ , or (–∞, 2].
Figure 2.50: Solving
3
14
2
x
x−≥−
The TI-82 is capable of shading the region above or below a graph or between two graphs. For example, to graph y
≥ x
2
–1, first graph the function y = x
2
–1 as Y
1
. Then press 2nd DRAW 7 2nd Y-
VARS
1 1 , 10 , 2 ) ENTER (see
Figure 2.51). These keystrokes instruct the TI-82 to shade the region above y = x
2
–1 and below y = 10 (chosen
because this is the greatest y-value in the graph window) with shading resolution value of 2. The result is shown in
Figure 2.52.
To clear the shading, press 2nd DRAW 1.
Figure 2.51: DRAW Shade Figure 2.52: Graph of y ≥ x
2
–1
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