The function f is called constant function, if every element of A has the same image in B.

Range of a constant function is a singleton set.

Let A  =  {x, y, u, v, 1 }, B  =  {3, 5, 7, 8, 10, 15}.

The function f : A ---> B defined by f (x) = 5 for every x belonging to A is a constant function.

The figure given below represents a constant function.

Solved Problems 

Problem 1 : 

Let f : X ----> Y. X, Y and f are defined as 

X  =  {a, b, c, d}

Y  =  {d, e, f}

f  =  {(a, e), (b, e), (c, e)}

Is f constant function ? Explain.

Solution : 

Write the elements of f (ordered pairs) using arrow diagram as shown below. 

In the above arrow diagram, every element of X has the image "e" in Y.  

So, f is a constant function. 

Problem 2 :  

Let f : A ----> B. A, B and f are defined as 

A  =  {1, 2, 3, 4}

B  =  {5, 6, 7, 8}

f  =  {(1, 8), (2, 6), (3, 5), (4, 7)}

Verify whether f is a function. if so, what type of function is f ?

In the above arrow diagram, every element of A does not have the same image in B.  

So, f is not a constant function. 

Related Topics

One to one or Injective function

Onto or Surjective function

One to one and Onto or Bijective function

Into function

Identity function

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