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EL-9900 Graphing Calculator
11-2
Solving Rational Function Inequalities
A rational function f (x) is defined as the quotient where p (x) and q (x) are two
polynomial functions such that q (x) ≠ 0. The solutions to a rational function inequality can
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.
Solve a rational inequality.
Example
Solve
≤
2 by graphing each side of the inequality as an individual function.
1 Enter y = for Y1. Enter y = 2
for Y2.
2 Set up the shading.
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.
4
Find the intersections, and solve the
inequality.
The intersections are when
x = -1.3, -0.8, 0.8, and 1.3.
The solution is all values of
x such that x
≤
-1.3 or
-0.8
≤
x
≤
0.8 or x
≥
1.3.
Do this four times
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.
x
1 - x
2
x
1- x
2
Y=
a
/b
MATH
B
1
1
2
G1
2
2nd F CALC
2nd F
DRAW
—
ENTER
q (x)
p (x)
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:
(
)
ENTER
A
ZOOM
7
ALPHA
Notes
Step & Key Operation
Display
X/
/T/n
A1
2nd F
2nd F
VARS
VARS
ENTER
ENTER
A
2
3
View the graph.
GRAPH
x
2
X/
/T/n