To find the domain and range of a graph:
- The domain is the set of all possible x-values (inputs) of the graph. To find it, look at the graph from left to right and identify the smallest and largest x-values covered. The domain includes all x-values between these points, noting if endpoints are included or not.
- The range is the set of all possible y-values (outputs) of the graph. To find it, look at the graph from the bottom to the top and identify the smallest and largest y-values covered. The range includes all y-values between these points, with attention to whether endpoints are included.
Key points:
- Check for any breaks, holes, or asymptotes in the graph that may exclude certain x or y values from the domain or range.
- Use interval notation to express the domain and range.
- The domain is based on horizontal extent; the range is based on vertical extent.
For example, if a graph stretches from x = -2 to x = 2 with no breaks, the domain is [−2,2][-2,2][−2,2]. If vertically it stretches from y = 1 to y = 5, the range is $$$$.
In summary:
- Domain: Look at x-values covered from left to right.
- Range: Look at y-values covered from bottom to top.
This is the general process to find domain and range from any graph of a function or relation.
