Evaluating Absolute Value Functions - Sharp EL-9650 Handbook

Evaluating Absolute Value Functions

The absolute value of a real number x is defined by the following:
|x| = x if x
-x if x
Note that the effect of taking the absolute value of a number is to strip away the minus sign
if the number is negative and to leave the number unchanged if it is nonnegative.
Thus, |x| 0 for all values of x.
Example
Evaluate various absolute value functions.
1.
Evaluate |- 2(5-1)|
2.
Is |-2+7| = |-2| + |7|?
Evaluate each side of the equation to check your answer.
Is |x + y| =|x|+ |y| for all real numbers x and y ?
If not, when will |x + y| = |x|+|y| ?
6-9 |6-9|
3.
Is | | =
1+3
|1+3|
Evaluate each side of the equation to check your answer. Investigate with
more examples, and decide if you think |x / y|=|x|/|y|
Before There may be differences in the results of calculations and graph plotting depending on the setting.
Starting
Return all settings to the default value and delete all data.
Step & Key Operation
(When using EL-9650/9600c)
*Use either pen touch or cursor to operate.
1
1
Access the home or computation
-
screen.
1
2
Enter y = |-2(5-1)| and evaluate.
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-
(
B 1
MATH
* *
1 )
ENTER
2
1
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Evaluate|-2 + 7|. Evaluate|-2|+|7|.
CL
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( )
1
MATH
*
-
1 ( )
MATH
*
1 7
ENTER
*
EL-9650/9600c/9450/9400 Graphing Calculator
0
0
?
(When using EL-9650/9600c)
) —
2 ( 5
+
2 7
ENTER
+
2
MATH
Display
The solution is + 8.
|-2 + 7| = 5, |-2| + |7| = 9
|-2 + 7|
Notes
|-2| + |7|.
8-5