I'm having trouble. |x+y|=2 is the problem. I'm supposed to graph this and find x and y intercepts. I know |x| is v shaped but this one puzzles me. Thanks in advance.
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Well, let's try graphing this exactly the same way we'd graph any other function. I can tell you right now that it won't be a function, because it fails the vertical line test, but that's okay. You can still graph relations. When graphing functions, one common and very useful way is to make a table. Pick some x-values, and fill in the corresponding y-values. Graph these points and see if you can get a feel for what the function looks like. If needed, graph a few points in between to be sure you've got it right. I'll start a few and leave you to finish:
Let x = 0. The relation tells us that |0+y| = 2. Therefore, we conclude that y = ±2. So graph the points (0, 2) and (0, -2).
Let x = 1. The relation tells us that |1+y| = 2. Therefore, we conclude that y = 1 or y = -3. So graph the points (1, 1) and (1, -3).
Let x = 2. The relation tells us that |2+y| = 2. Therefore, we conclude that y = 2 or y = -4. So graph the points (2, 0) and (2, -4).
Are you seeing a pattern? If not, maybe graph a few more and see if starts to fill in. Based on this pattern, what do you conclude the overall graph of |x + y| =2 would look like?
