Solving Rational Function Inequalities - Sharp EL-9900 Handbook Vol. 1 Operation Manual

Solving Rational Function Inequalities

A rational function f (x) is defined as the quotient
polynomial functions such that q (x)
be obtained graphically using the same method as for normal inequalities. You can find the
solutions by graphing each side of the inequalities as an individual function.
Example
Solve a rational inequality.
x
Solve 2 by graphing each side of the inequality as an individual function.
1 - x 2
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
x
1
Enter y =
2
1- x
for Y2.
Y= B 1
MATH
x
n
—
1
X/ /T/
2
Set up the shading.
G 1
2nd F DRAW
A
2nd F VARS ENTER
2nd F VARS ENTER
3
View the graph.
GRAPH
4
Find the intersections, and solve the
inequality.
2 Do this four times
2nd F CALC
The EL-9900 allows the solution region of inequalities to be indicated visually
using the Shade feature. Also, the points of intersections can be obtained
easily.
0. The solutions to a rational function inequality can
ZOOM
for Y1. Enter y = 2
n
a /b
X/ /T/
2 2
ENTER
A 1
2
EL-9900 Graphing Calculator
p (x)
where p (x) and q (x) are two
q (x)
( )
A
ENTER ALPHA
Display
Since Y1 is the value "on the
bottom" (the smaller of the
two) and Y2 is the function
"on the top" (the larger of the
two), Y1 < Y < Y2.
The intersections are when
x = -1.3, -0.8, 0.8, and 1.3.
The solution is all values of
x such that x
-0.8
7
Notes
-1.3 or
0.8 or x 1.3.
x
11-2