# Functions

## Algebra-1 Worksheets

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}.

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## 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-

- {(-2, -5), {2, 2), (-2, 3), (3, 5)}
- {(0, 5), {2, 3), (3, 4), (4, 5)}
- {(-4, 5), {-3, 2), (0, 3), (2, 5), (5,8)}
- {(1, 11), {4, 15), (1, 17), (2, 5), (5, 8), (7, 11)}
- Find domain of function
*f*(*x*) = 2*x*^{5}+ 7*x*^{4}– 3*x*^{3}+ 4*x*^{2}+ 9

### Answer Key

- Not a function
- Function
- Function
- Not a function
- All real numbers or

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