A line with undefined slope...
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A line with undefined slope...
If I have a line with undefined slope, what would the range of that equation be?
 dudiobugtron
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 Location: The Outlier
Re: A line with undefined slope...
I think it's not a function, so doesn't have a 'range'.
But if you're looking at something like the relation xRy iff x=4, then set of possible values for y is the same as whatever set the relation is defined on. eg: the Real numbers.
But if you're looking at something like the relation xRy iff x=4, then set of possible values for y is the same as whatever set the relation is defined on. eg: the Real numbers.

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: A line with undefined slope...
The answer to the question depends on whether you mean that the slope of the line is undefined because the line is vertical, in which case the range is all of R, or if you mean that the slope has not been defined yet, in which case the range is all of R except if the slope is 0, in which case the range is the specific value the function is defined to be at 0.
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: A line with undefined slope...
We're also assuming that the line is a *straight* line, rather than a potentially curved one. This is probably a safe assumption, but just for the sake of covering bases it might be worth mentioning.
Otherwise, you can end up with situations like a circle, which has a couple points of undefined slope even though the range is just some interval.
Otherwise, you can end up with situations like a circle, which has a couple points of undefined slope even though the range is just some interval.
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