I’m sort of confused on how to state and find the domain and range of this graph

You have a special type of function, so you have to express the domain and range of each interval. Every aspect of this graph is closed, so you will only use brackets when writing your answers. Hence, you get [30,5] for the first interval, since there is a horizontal distance of 30 and a vertical distance of 5. You repeat the same process for each interval.