
If in an equation of nth degree, the term with x^{n} is absent, then the coefficient of the next higher power of x when equated to zero, gives horizontal asymptotes (provided it must not be a constant)
For example, x^{3} + 3xy^{2 }+ y^{2} + 2x + y = 0 has no horizontal asymptote as x^{3} is present
For example x^{2 }y^{3} + x^{3}3y^{2} = x^{3} + y^{3}
This equation is a 5^{th} degree equation. Since x^{5}
is absent, we have coefficient of x^{3} is (y^{2}
 1)= 0 i.e. y = ± 1 are two asymptotes parallel to xaxis i.e.
horizontal asymptotes.
Note that the ‘Oblique asymptotes’ concept is beyond the scope of this book.
Example 1 Sketch the graph of the function x^{2}
+ 2x  5 (1) using it determine the real roots of x^{2}
+ 2x  5 = 0 (2) Find y when x = 2.5
Solution :
1) Let y = f(x) = x^{2} + 2x  5
x 
 4 
3 
2 
1 
0 
1 
2 
3 
y = f(x) 
3 
2 
5 
6 
5 
2 
3 
10 
The curve is a parabola which cuts xaxis in points whose abscissa is between 1 and 2 and a point whose abscissa is between 3 and 4. From the graph the roots are x =1.5 and x = 3.5. From the graph y = 6.25 when x = 2.5.

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
