1.3 Rules For Drawing The Graph Of A Curve (representing
a function) :
Symmetry :

If x is replaced by x but the equation remains
the same, the graph shall be symmetrical about yaxis.

If y is replaced by  y but the equation
remains the same, the graph shall be symmetrical about xaxis.
For example : y^{2} = 4ax is symmetrical
about xaxis.
x^{2} + y^{2} = a^{2}
is symmetrical about both x and y axis.

If both x and y are changed by  x and 
y respectively and simultaneously,and equation is unchanged,
then the graph is symmetrical about the origin and symmetrical
in opposite quadrants .
In above illustration, x^{2} + y^{2}
= a^{2} is a standard circle having center at the
origin with radius ‘a’ units.

When x and y are interchanged and equation
remains the same, the curve is symmetrical about the line
y = x.
Clearly the curve x^{3}
+ y^{3} = 3axy is symmetrical about y = x.
Intercepts on the axes : Put y = 0 in
the equation to find xintercept and put x = 0 to find yintercept.
Extent of the curve : Know the domain
of the curve that exists. This gives the horizontal extent.
Know the range, this gives the vertical extent of the curve
(i.e. function)
Tangent at the origin : If the curve
passes through origin, then equate its lowest degree term to
zero. This gives the tangents at the origin.
For example, y^{2} = 4ax, passes
through origin
\ Taking
4ax = 0 gives x = 0 ( i.e. yaxis )
Similarly x^{2 } = 4by, passes
through origin
\ Taking
4by = 0 gives y = 0 ( i.e. x  axis )
The curve x^{3} + y^{3}
= 3axy also passes through origin.
\ Taking
3axy = 0 or x = 0 and y = 0 i.e. both axes touch the curve at
the origin.
Asymptotes : The value of x which makes
y infinitely large gives a straight line which touches a branch
of the curve at infinity. Similarly for y.
Such a straight line is called an Asymptote
to the curve.

To locate vertical asymptotes (parallel to
yaxis), if an equation of nth degree, the term with yn is
absent, then the coefficient of the next highest power of
y when equated to zero, gives the vertical asymptotes (provided
this coefficient must not be a constant.
For example, x^{3}+ 3xy^{2}
+ y^{2} + 2x + y = 0
Since y^{3} is absent. The
coefficient of y^{2} is ( 3x + 1 ) = 0 which the asymptote
parallel to yaxis i.e. vertical asymptote.

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
