f ( ) = ... f ( ) = ... f ( ) = ... Solution The completed table is given by f ( ) = f ( ) = f ( ) = f ( ) = f ( ) = f ( ) = f ( ) = MATHEMATICS .
. Some functions and their graphs Identity function Let R be the set of real numbers. Define the real valued function f : R → R by y = f ( x ) = x for each x ∈ R . Such a function is called the identity function .
Here the domain and range of f are R . The graph is a straight line as shown in Fig . . It passes through the origin.
Fig . Fig . Constant function Define the function f : R → R by y = f ( x ) = c , x ∈ R where c is a constant and each x ∈ R . Here domain of f is R and its range is { c }.
RELATIONS AND FUNCTIONS The graph is a line parallel to x -axis. For example, if f ( x )= for each x ∈ R , then its graph will be a line as shown in the Fig . . (iii) Polynomial function A function f : R → R is said to be polynomial function if for each x in R , y = f ( x ) = a + a x + a x + ...+ a n x n , where n is a non-negative integer and a , a , a ,..., a n ∈ R .
The functions defined by f ( x ) = x – x + , and g ( x ) = x + x are some examples of polynomial functions, whereas the function h defined by h ( x ) = x + x is not