unit 1 differential calculus - IGNOU

The role that the graph of a function plays in the study of the function will
become clear as we proceed further. In the meantime let us consider some
more examples of functions and their graphs.
A Constant Function
A simple example of a function is a constant function. A constant
function sends all the elements of the domain to just one element of
the co-domain.
For example, let f : R → R be defined by f (x) = 1.
Alternatively, we may write
f : x → 1 for all x ∈ R
The graph of f is as shown in Figure 1.3.
1
0
y
f (x) = 1
Figure 1.3
It is the line y = 1.
In general, the graph of a constant function y : x → c is a straight line
which is parallel to the x-axis at a distance of c units from it.
The Identity Function
Another simple but important example of a function is a function
which sends every element of the domain to itself.
Let X by any non-empty set, and f be the function of X defined by
setting f (x) = x, for all x ∈ X.
This function is known as the identity function on X and is denoted
by IX.
The graph of IR, the identity function of R, is shown in Figure 1.4. It is
the line y = x.
0
y
Figure 1.4
y = x
x
x
Differential Calculus
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