CONSTANT FUNCTION

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

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.