Sharp EL9900 manual Solving Rational Function Inequalities

EL-9900 Graphing Calculator

Solving Rational Function Inequalities

p (x)

A rational function f (x) is defined as the quotient q (x)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.

Example

Solve a rational inequality.

Solve	x	≤ 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:

ZOOM A

(

ENTER ALPHA

)

7

Step & Key Operation Display Notes

1	Enter y =	x	for Y1. Enter y = 2
		1- x 2
	for Y2.

Y= MATH B 1 a/b X//T/n

1 — X//T/n x2 ENTER 2

2Set up the shading.

2nd F DRAW G 1

2nd F VARS A ENTER A 1

2nd F VARS ENTER 2

3View the graph.

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.

GRAPH

4Find the intersections, and solve the inequality.

2nd F CALC 2 Do this four times

The intersections are when

x= -1.3, -0.8, 0.8, and 1.3. The solution is all values of

xsuch that x ≤ -1.3 or -0.8 ≤ x ≤ 0.8 or x ≥ 1.3.

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.

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