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EL-9900 Graphing Calculator
10-1
Slope and Intercept of Absolute Value Functions
The absolute value of a real number x is defined by the following:
|x| = x if x
≥
0
-x if x
≤
0
If n is a positive number, there are two solutions to the equation |f (x)| = n because there
are exactly two numbers with the absolute value equal to n: n and -n. The existence of two
distinct solutions is clear when the equation is solved graphically.
An absolute value function can be presented as y = a|x - h| + k. The graph moves as the
changes of slope a, x-intercept h, and y-intercept k.
Consider various absolute value functions and check the relation between the
graphs and the values of coefficients.
Example
1. Graph y = |x|
2. Graph y = |x -1| and y = |x|-1 using Rapid Graph feature.
1-1
Enter the function y =|x| for Y1.
Notice that the domain of f(x)
= |x| is the set of all real num-
bers and the range is the set of
non-negative real numbers.
Notice also that the slope of the
graph is 1 in the range of X > 0
and -1 in the range of X
≤
0.
1-2
View the graph.
2-1
Enter the standard form of an abso-
lute value function for Y2 using the
Rapid Graph feature.
2-2
Substitute the coefficients to graph
y = |x - 1|.
Y=
Y=
ENTER
ENTER ENTER2nd F SUB
MATH
B
1
11
0
GRAPH
Before
Starting
There may be differences in the results of calculations and graph plotting depending on the setting.
Return all settings to the default value and delete all data.
Set the zoom to the decimal window: ( )
ZOOM
ENTER
2nd F
A
7
Notes
Step & Key Operation
Display
ALPHA
H
A
ALPHA
—
MATH
1B
ALPHA
+ K
X/
/T/n
X/
/T/n