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Example 2 Discuss the equation (x2-1)y = 1 with regard to intercepts, symmetry, domain and range and asymptotes. Plot a graph of its Locus.

Solution :

Let

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1) Intercepts   i) y = 0 Þ No x- intercept
ii) x = 0 Þ y = -1

2) Symmetry i) x-axis : No symmetry as -y for y changes the
equation.

ii) y-axis : Symmetrical. Since -x for x does not
change the equation.

iii) Origin : No symmetry

3) i)     Domain ( or extent ) : All x ( x ¹ ± 1 )

ii)    Range : All y ( g (y) ³ 0 )

g (y) > 0 « > 0

Thus,

 y 1 0 - ½ -1 -2 g(y) + undefined - 0 +

The range is all y > 0 or £ -1

4) Asymptotes i) Vertical : x = ± 1

ii) Horizontal : y = 0

Index

Introduction

1.1 Functions And Mapping
1.2 Functions, Their Graphs and Classification
1.3 Rules for Drawing the Graph of a Curve
1.4 Classification of Functions
1.5 Standard Forms for the equation of a straight line
1.6 Circular Function and Trigonometry

Chapter 2