Domain, Range, Even, and Odd Functions
Domain and Range
The domain of a function is all x-values where is defined.
The range of a function is all y-values where is defined.
To describe the domain and range of a function, you can use the following notations.
Interval Notation
Interval notation utilises [] and () to describe the end values of a function. Square brackets means it includes the end values of that interval, whereas round brackets do not include the end values.
Example
Find the domain of .
Inequalities and Other Formats
You can describe the domain and range of a function by using inequalities, such as . You can also describe it by saying , , and .
Even and Odd Functions
Even Functions
Even functions are symmetrical by the y-axis (creating a mirror line). This means that the graph does not change when it is reflected by the y-axis. Thus, for and , the y-value is the same.
This can be proved by following the rule .
Example
Determine whether is odd or even.
Odd Functions
Odd functions are symmetrical by the x-axis (establishing a mirror line). This means that if the graph is reflected by the x-axis, it does not change. Thus, for and , the values of y are flipped (e.g. , ).
This can be proved through following the rule .
Example
Determine whether is odd or even.
Warning
Be careful not to use to create . Always derive from