Sharp EL-9900 Handbook Vol. 1 Operation Manual page 42

Step & Key Operation
2
2 Is |x + y| = |x| +|y|? Think about
-
this problem according to the cases
when x or y are positive or negative.
If x 0 and y
[e.g.; (x, y) = (2,7)]
If x 0 and y
[e.g.; (x, y) = (-2, 7)]
If x 0 and y
[e.g.; (x, y) = (2, -7)]
If x 0 and y
[e.g.; (x, y) = (-2, -7)]
6-9
3
1 Evaluate . Evaluate
-
1+3
CL
MATH 1
+
1
—
1 6
MATH
+
1 1
MATH
3
2 Is |x /y| = |x|/|y|?
-
Think about this problem according
to the cases when x or y are positive
or negative.
If x 0 and y
[e.g.; (x, y) = (2,7)]
If x 0 and y
[e.g.; (x, y) = (-2, 7)]
If x 0 and y
[e.g.; (x, y) = (2, -7)]
If x 0 and y
[e.g.; (x, y) = (-2, -7)]
The EL-9900 shows absolute values with | |, just as written on paper, by using
the Equation editor. The nature of arithmetic of the absolute value can be
learned through arithmetical operations of absolute value functions.
10-4
0 |x +y| = |2 + 7| = 9
|x|+|y| = |2| + |7| = 9
0
|x +y| = |-2 + 7| = 5
|x|+|y| = |-2| + |7| = 9
0
|x +y| = |2-7| = 5
|x|+|y| = |2| + |-7| = 9
0
|x +y| = |-2-7| = 9
|x|+|y| = |-2| + |-7| = 9
Therefore |x +y|=|x|+|y|when x
and when x
6-9
.
1+3
a /b
—
6 9
3 ENTER
a /b
9
3
ENTER
0
|x /y| = |2/7| = 2/7
|x|/|y| = |2| /|7| = 2/7
0
|x /y| = |(-2)/7| = 2/7
|x|/|y| = |-2| /|7| = 2/7
0
|x /y| = |2/(-7)| = 2/7
|x|/|y| = |2| /|-7| = 2/7
0
|x /y| = |(-2)/-7| = 2/7
|x|/|y| = |-2| /|-7| = 2/7
The statement is true for all y
EL-9900 Graphing Calculator
Display
0 and y 0.
6-9
1+3
6-9
1+3
Notes
|x + y| = |x| + |y|.
|x + y| |x| + |y|.
|x + y| |x| + |y|.
|x + y| = |x| + |y|.
0 and y 0,
6-9
= 0.75 , = 0 .75
1+3
6-9
=
1+3
|x /y| = |x| / |y|
|x /y| = |x| / |y|
|x /y| = |x| / |y|
|x /y| = |x| / |y|
0.