Functions

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.

Example:

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}.

Example:

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

Example:

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

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