To solve this question first of all we need to understand what is a domain and a range of a function.
- Domain: All x-axis values the function uses on its graph.
- Range: All y-axis values the function uses on its graph.
Once we understand that, we can analyze our graph. We can identify that there are also two kinds of "dots". The blue dot that means the function includes that value and the white dot that means the function does not include it.
As part of an interval we can use a simple notation:
-Blue dots: "[" or "]"
-White dots: "(" or ")"
Now we can write our domain and range as follows:
Domain:
Analyzing x-axis from left to right we have a white dot which means an open interval "(" for -3 and the function goes until -2 where we have a blue dot which means a closed interval "]". So this first interval is represented by (-3,-2].
The next interval is closed in 0 "[" and opened in 5 ")" So this second interval is represented by [0,5).
As our function is a union between both intervals we can represent our domain as follows:
Range:
Analyzing y-axis from the bottom to the top, we have an interval opened in -1 and closed in 2. So this first interval is represented by (-1,2].
For the second one we are closed in 3 and opened in 4. So this first interval is represented by [3,4).
As our function is a union between both intervals we can represent our range as follows:
And thats are our domain and range for this question.