Slope And Intercept Of Absolute Value Functions - Sharp EL-9900 Handbook Vol. 1 Operation Manual

Slope and Intercept of Absolute Value Functions

The absolute value of a real number x is defined by the following:
|x| = x if x
-x if x
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.
Example
Consider various absolute value functions and check the relation between the
graphs and the values of coefficients.
1.
Graph y = |x|
2.
Graph y = |x -1| and y = |x|-1 using Rapid Graph feature.
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.
Set the zoom to the decimal window:
Step & Key Operation
1
1
- Enter the function y =|x| for Y1.
Y= B 1
MATH
1
2
View the graph.
-
GRAPH
2
1
- Enter the standard form of an abso-
lute value function for Y2 using the
Rapid Graph feature.
Y=
ALPHA
n
—
X/ /T/ ALPHA
2
2
Substitute the coefficients to graph
-
y = |x - 1|.
1
2nd F SUB ENTER
0
ENTER
10-1
0
0
ZOOM
n
X/ /T/
A B 1
MATH
+
H K
ALPHA
1
ENTER
EL-9900 Graphing Calculator
( )
A 7
ENTER 2nd F
Display
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
Notes
0.