Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 12 : Curve sketching [Section 12.2]
12.2
Curve sketching
In this section we shall see how the various tools of calculus developed so far help us to draw a graph of the function . The aim is to get a visualization of the function from is formula . In addition to the various properties that we have analyzed so far some more properties of interest to sketch the graph of a function are the following:
12.2.1
Symmetries:
(i)
A function is symmetric with respect to y-axis if for every in the domain of .
Such a function is also called an even function. For such a function, one need to draw the graph of only , and reflect the graph about y-axis to get it for .
(ii)
A function is symmetric with respect to origion if for every . Such a function is also
called an odd function . For such a function also, one need to draw the graph for only. For , its graph is obtained by reflecting against both x-axis and then y-axis.
. The aim is to get a visualization of the function from is formula 
. In addition to the various properties that we have analyzed so far some more properties of interest to sketch the graph of a function are the following: 
is symmetric with respect to y-axis if 
for every 
in the domain of 
. 
only 
, and reflect the graph about y-axis to get it for 
. 
is 
for every 
. Such a function is also 
only. For 
, its graph is obtained by reflecting against both x-axis and then y-axis. 
is symmetric about y-axis as 
. 
is symmetric about origion as 
