In this lesson we will at the domain and range of functions
The domain of a function is the set of all the allowable values that can be used as the input to the function.
The range of a function is the set of values that can be obtained as the output of the function.
Find the domain and range of
For f(x) to be a real number
1 – x2 ≥ 0 x2 ≤ 1
–1 ≤ x ≤ 1
Therefore, the domain is –1 ≤ x ≤ 1
The smallest value for f(x) is when x = 1 or –1
The largest value for f(x) is when x = 0
Therefore, the range is 0 ≤ y ≤ 1
Find the domain of
If (x – 2)(x + 5) = 0 then f(x) would be undefined.
For (x – 2)(x + 5) = 0, either x = 2 or x = –5
Therefore, the domain consist of all real numbers, except 2 and –5
Domain and Range
An important part of understanding functions is understanding their domain and range. Domain and range are all the possible x-values and y-values of the function, and can often be described easily by looking at a graph. In order to grasp domain and range, students must understand how to determine if a relation is a function and interpreting graphs.
Reading Domain and Range of a Relation From a Graph
Finding the Domain of a Function
We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.