2. If in an equation of nth degree, the term with xⁿ 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, x³ + 3xy² + y² + 2x + y = 0 has no horizontal asymptote as x³ is present

   For example x² y³ + x³3y² = x³ + y³

   This equation is a 5^th degree equation. Since x⁵ is absent, we have coefficient of x³ is (y² - 1)= 0 i.e. y = ± 1 are two asymptotes parallel to x-axis 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 x² + 2x - 5 (1) using it determine the real roots of x² + 2x - 5 = 0 (2) Find y when x = 2.5

Solution :

1) Let y = f(x) = x² + 2x - 5

The curve is a parabola which cuts x-axis 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