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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
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
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