Sharp EL-9650 - Page 44

EL-9650/9600c/9450/9400 Graphing Calculator
NotesStep & Key Operation
(When using EL-9650/9600c)
*Use either pen touch or cursor to operate.
Display
(When using EL-9650/9600c)
= 0.75 , = 0 .75
8-5
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 ≥ 0
[e.g.; (x, y) = (2,7)]
If x
≤ 0 and y ≥ 0
[e.g.; (x, y) = (-2, 7)]
If x
≥ 0 and y ≤ 0
[e.g.; (x, y) = (2, -7)]
If x
≤ 0 and y ≤ 0
[e.g.; (x, y) = (-2, -7)]
|x +y| = |2 + 7| = 9
|x|+|y| = |2| + |7| = 9
➞|x + y| = |x| + |y|.
|x +y| = |-2 + 7| = 5
|x|+|y| = |-2| + |7| = 9
➞|x + y| ≠ |x| + |y|.
|x +y| = |2-7| = 5
|x|+|y| = |2| + |-7| = 9
➞|x + y| ≠ |x| + |y|.
|x +y| = |-2-7| = 9
|x|+|y| = |-2| + |-7| = 9
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3-1
Evaluate . Evaluate .
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 ≥ 0
[e.g.; (x, y) = (2,7)]
If x
≤ 0 and y ≥ 0
[e.g.; (x, y) = (-2, 7)]
If x
≥ 0 and y ≤ 0
[e.g.; (x, y) = (2, -7)]
If x
≤ 0 and y ≤ 0
[e.g.; (x, y) = (-2, -7)]
|x /y| = |2/7| = 2/7
|x|/|y| = |2| /|7| = 2/7
➞|x /y| = |x| / |y|
|x /y| = |(-2)/7| = 2/7
|x|/|y| = |-2| /|7| = 2/7
➞|x /y| = |x| / |y|
|x /y| = |2/(-7)| = 2/7
|x|/|y| = |2| /|-7| = 2/7
➞|x /y| = |x| / |y|
|x /y| = |(-2)/-7| = 2/7
|x|/|y| = |-2| /|-7| = 2/7
➞|x /y| = |x| / |y|
The statement is true for all y ≠ 0.
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The EL-9650/9600c/9450/9400 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.
6-9
1+3
6-9
1+3
6-9
1+3
6-9
1+3
6-9
1+3
6-9
1+3
➞ =
➞|x + y| = |x| + |y|.
Therefore |x +y|=|x|+|y|when x
≥ 0 and y ≥ 0,
and when x
≤ 0 and y ≤ 0.
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