Before going to the range, it's better to discuss first about the symbols used in inequality expressions. These equations contain <, >, ≤ and ≥ in their equations. That is why there are solid and hollow figure when they are graphed. If the line is solid, that means points along that line are part of the solution. If not, then they are not part of the solution. The same applies for solid points and hollow points.
Now, the domain and range of a given function is basically the coverage of their x and y values that are part of the solution. If the point is along the solid lines and points, the domain or range is expressed either in [ or ], depending where it starts and ends. If the point is along the hollow lines and points, the domain or range is expressed either in ( or ), depending where it starts and ends. The ∪ symbol is added to connect domains and ranges through discontinuities.
Looking at the leftmost line, it starts from the hollow point (-7,-4) and ends on the solid point (-3,3). The range for this part is expressed as (-4,3]. Looking the rightmost line, it starts from the hollow point (-1,-3) and ends at the solid point (2,-8). The range for this part is expressed as (3,8]. Connecting the two ranges, the answer would be (-4,3)U(3,8].