For the Domain Hold a ruler, or some similar object, vertically on the left side of the graph. Now slowly move it to the right and mark down the intervals of x where the ruler would be crossing the graph. In this case, the graph heads to the left forever, so we start by thinking of x as -∞. As we move right, the graph is there until we hit x=-1 where there are those open circles indicating that no point exists there. So our first interval is (-∞, -1). As we continue, the ruler intersects the graph from just beyond -1 until we get to more open circles at x=4. So that interval is (-1, 4). After that the graph continues forever to the right which we write as ∞. So that interval is (4, ∞). Putting them together, we get... (-∞, -1) ∪ (-1, 4) ∪ (4, ∞) So the domain is every value of x from -∞ to ∞ except for -1 and 4. For the Range Do the same thing but in the vertical direction. Start with the ruler held horizontally at the bottom of the graph and move up while keeping track of the intervals of y where the ruler crosses the graph. Answer from Bascna on reddit.com