Graphing without the YDate: 01/28/2004 at 20:43:42 From: Stephanie Subject: Algebra I need help with graphing inequalities. There is a certain one that doesn't make any sense to me. It is: x > -5 There is no "y", so how do I do it? Date: 01/29/2004 at 09:48:37 From: Doctor Ian Subject: How do you deal with a missing y? Hi Stephanie, There are a couple of ways to look at this. One is to forget about the coordinate plane, and go back to the number line. On a number line, you want to emphasize (by making it bolder) the part of the line that satisfies the inequality, e.g., to graph 3 < x < 7 - I would do this: <--|--|--o===========*--|--|--> 1 2 3 4 5 6 7 8 9 Here the 'o' represents an open endpoint, meaning I can get almost down to 3, but never quite there; while the '*' represents a closed endpoint, meaning I can get all the way to 7. Does this make sense? Now, suppose I really want to graph this on a coordinate plane. Let's think for a moment about the equation of a vertical line on the plane. That might look like x = 4 right? There's no y! So what can we do? Well, when no constraints are placed on y, it means that y can take _any_ value at all. In the case of a vertical line, y can be 2, giving us the point (4,2) or it can be 6.3, giving us the point (4,6.3) and so on. When we fill in _all_ the possible values of y, we get a vertical line. In the case of an inequality, we get a vertical line through each possible value of x. That would include when x is 4, | | | <--|--|--o==|========*--|--|--> 1 2 3 | 5 6 7 8 9 | | and when x is 5.3, | | | | | | <--|--|--o==|===|====*--|--|--> 1 2 3 | 5| 6 7 8 9 | | | | and every other possible value of x in the specified range. When we fill all those lines in, what will we get? We'll end up with a shaded region of the plane, o###########* o###########* o###########* <--|--|--o###########*--|--|--> 1 2 o###########* 8 9 o###########* o###########* Here, the 'o's would normally be drawn as a dashed line, showing that we can't quite get over to x = 3; and the '*'s would be drawn as a solid line, to show that we can get all the way to x = 7. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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