Sharp EL-9650, EL-9400, EL-9600c manual Solving Rational Function Inequalities

Page 47

EL-9650/9600c/9450/9400 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.

x

Solve 1 - x 2 2 by graphing each side of the inequality as an individual function.

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

(When using EL-9650/9600c)

(When using EL-9650/9600c)

 

*Use either pen touch or cursor to operate.

 

 

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

 

 

x 2

 

 

 

ENTER

 

*

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2Set up the shading.

2nd F DRAW G * 1 *

* *

View the graph.

3

GRAPH

4Find the intersections, and solve the inequality.

2nd F CALC 2 * Do this four times

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

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

The EL-9650/9600c/9450/9400 allows the solution region of inequalities to be indicated visually using the Shade feature. Also, the points of intersections can be obtained easily.

9-2

Image 47
Contents EL-9650/9600c/9450/9400 Contents Always read Before Starting Read this firstIntroduction Using this HandbookSlope and Intercept of Linear Equations Enter the equation y = x for Y2 Parallel and Perpendicular Lines 2View the graphs Slope and Intercept of Quadratic Equations 1Change the equation in Y2 to y = x 2+2 Shifting a Graph of Quadratic Equations 1Move the graph y = x 2 to the right by 1Access the Solver feature This screen will appear a few 4Enter the values L=15,000, I=0.09, N=48 Access the Solver feature 200 15π 10π1Access the Solver feature 5Solve for the height and enter a starting point Graphing Polynomials and Tracing to Find the Roots 1Move the tracer near the left-hand root Graphing Polynomials and Jumping to Find the Roots EL-9650/9600c/9450/9400 Graphing Calculator Solving a System of Equations by Graphing or Tool Feature 1Access the Tool menu. Select the number of variables Entering and Multiplying Matrices Enter a 3 x 3 matrix B Solving a System of Linear Equations Using Matrices 17 0.83 = 0.5 0.5 17 0.17 Solving Inequalities 1Enter y = 34 2x for Y1 and y = 5 x for Y2 2x 5 ≥ Solving Double Inequalities= 2x 5 and y = 7 intersect at 6,7 + y ≤ System of Two-Variable Inequalities+ y ≥ Graphing Solution Region of InequalitiesContinuing key operations omitted If x ≥ Slope and Intercept of Absolute Value Functions3View the graph Shifting a graph of Absolute Value Functions = x y = Solve an absolute value equation 5 4x = Solving Absolute Value EquationsSolving Absolute Value Inequalities = -4, y = 2Set up shadingEvaluating Absolute Value Functions Evaluate Graphing Rational Functions + 1x Solving Rational Function Inequalities = y 2 + 2 = y = +- √ x + Graphing Parabolas1Change to parametric mode Graph x 2 2x + y 2 + 4y = Graphing Circles3Turn off Y1 so that it will not graph Graphing Ellipses View the graph in the new window Graphing Hyperbolas Zoom out the screen Key pad for the Sharp EL-9650/9600c Calculator Key pad for the Sharp EL-9450/9400 Calculator We thank you for your cooperation in this project Step Sharp Corporation OSAKA, Japan
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EL-9650, EL-9600c, EL-9400 specifications

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