Solving Rational Function Inequalities - Sharp EL9600C - Graphing Calculator Handbook

Solving Rational Function Inequalities

A rational function f (x) is defined as the quotient
polynomial function 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.
2
1 - x
Before There may be differences in the results of calculations and graph plotting depending on the setting.
Start
Return all settings to the default value or to delete all data.
Set the zoom to the decimal window:
Step & Key Operation
(When using EL-9600)
*Use either pen touch or cursor to operate.
x
1
Enter y =
2
1- x
for Y2.
Y= MATH B 1
*
n
x
1 — X/ /T/
2
Set up the shading.
1
2nd F DRAW G
*
— —
*
3
View the graph.
GRAPH
4
Find the intersections, and solve the
inequality.
2 Do this four times
2nd F CALC
*
The EL-9600/9400 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
(
A
ZOOM
*
(When using EL-9600)
for Y1. Enter y = 2
a /b n
X/ /T/
* *
2
ENTER 2
*
*
—
*
EL-9600/9400 Graphing Calculator
p (x)
where p (x) and q (x) are two
q (x)
)
7
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
Notes
-1.3 or
x 0.8 or x 1.3.
9-2