Math Help
The deer had to die!
Joined: Jun 2002
Posts: 39,835
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From: Fussa, Japan
For this one you have to know how range is defined. Is this function defined for all real numbers? If so, then it is discontinuous when x >= -1.
Similarly, this would be discontinuous outside the range if you are dealing with real numbers. So whenever x<-1.
In all cases, if x was limited by the definition in the right way(say x could only take on values >-1) then the function in problem #2 could never be discontinuous.
Similarly, this would be discontinuous outside the range if you are dealing with real numbers. So whenever x<-1.
In all cases, if x was limited by the definition in the right way(say x could only take on values >-1) then the function in problem #2 could never be discontinuous.
x pǝɹ
Joined: Feb 2003
Posts: 6,246
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From: Upstate
A discontinuous function occurs when there is no y-value for a given x. So it matters how x is defined. Typically in a math textbook they'll say something like
x is an element in the set of real numbers.
This means that x can take on any real number value. Since the problems definition limited the y-values for a specific range of x-values and if the textbook says x can take on any real number value, then there is a range of x's that have discontinuous y-values. Namely for those that are not defined (when x<=-1). But it depends on the assumptions the book makes.
x is an element in the set of real numbers.
This means that x can take on any real number value. Since the problems definition limited the y-values for a specific range of x-values and if the textbook says x can take on any real number value, then there is a range of x's that have discontinuous y-values. Namely for those that are not defined (when x<=-1). But it depends on the assumptions the book makes.
Last edited by Red X; Jan 21, 2009 at 04:26 PM.
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