A relation is called function if each input is related to exactly one output. There is a set of inputs and set of possible outputs in function.

Set of inputs is called domain and set of outputs is called range.


The relation, {(-2, -5), {1, 2), (3, 3), (4, 5)} is a function. Here every input is related to exactly one output.

Domain of function is {-2, 1, 3, 4} and range is {-5, 2, 3, 5}.



Here y is a function of x, we can write y = f(x). Every input is related to exactly one output.



Here relation is not a function because input -1 has two output values 15 and 18. 

Some Facts about Functions:        

  • Domain of polynomial is all real numbers.
  • Domain of a rational function is all real numbers except the x values for which denominator is getting 0. 

Check Point

Check whether given relation is a function or not-

  1. {(-2, -5), {2, 2), (-2, 3), (3, 5)}
  2. {(0, 5), {2, 3), (3, 4), (4, 5)}
  3. {(-4, 5), {-3, 2), (0, 3), (2, 5), (5,8)}
  4. {(1, 11), {4, 15), (1, 17), (2, 5), (5, 8), (7, 11)}
  5. Find domain of function f(x) = 2x5 + 7x4 – 3x3 + 4x2 + 9

Answer Key

  1. Not a function
  2. Function
  3. Function
  4. Not a function
  5. All real numbers or

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