Domain and Range
Domain
The domain of a function is the set of values of the independent variable (x) for which the function is defined.There are two common mathematical operations that are undefined: square root of a negative number and division by zero.
Because a square root cannot successfully act on a negative number, the domain of
![f(x) = squareroot of x f(x) = squareroot of x](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain1.png)
![x is greater than or equal to 0 x is greater than or equal to 0](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain1.5.png)
![domain 3 domain 3](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain2.png)
Division by zero is undefined; therefore values for x that produce a zero denominator are excluded from the domain. For instance, the function
![domain 3 domain 3](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain3.png)
![domain 4 domain 4](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain4.png)
![domain 5 domain 5](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain5.png)
![domain6 domain6](https://claregladwinresd.glk12.org/pluginfile.php/895/mod_book/chapter/68/Families_Of_Functions/Images/domain6.png)