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FlO-rida
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i am looking for a simple definition of discontinuity using the example 3/(x^2+x-6)
FlO-rida said:at x=2,-3. i understand that but when you say x=a what do u mean by that. can you show me a variable formula (using a, b and c) that would better explain this
FlO-rida said:so you are saying that a would be the constant. like in my example if we factor x^2+x-6 we get (x-2)(x+3), so how would that be undefined
FlO-rida said:sorry but i still don't get it, its not like we have a denominator of zero
FlO-rida said:wat i ment was it dosent cancel out or anything
FlO-rida said:ok then how would you compare that with a function that is not discontinuous like 1/(x+3)
FlO-rida said:sorry but i still don't get it, its not like we have a denominator of zero
rock.freak667 said:Say your function was
f(x)=1/(x-a)
Wouldn't you agree that [itex]\lim_{x \rightarrow a} = \infty[/itex] and so f(a) is undefined?
rock.freak667 said:cancel out with what?
f(x)=1/(x+3) is discontinuous at x=3.
A discontinuity is a point on a graph where the function is undefined or where the function has a jump or break in its graph. It is a point of discontinuity because the function is not continuous at that point.
Discontinuities can be caused by a variety of factors, such as a function being undefined at a certain point, a jump or break in the function's graph, or a vertical asymptote where the function approaches infinity or negative infinity.
There are three main types of discontinuities: removable, jump, and infinite. A removable discontinuity occurs when the function is undefined at a certain point but can be made continuous by filling in the hole. A jump discontinuity occurs when the graph has a sudden jump or break. An infinite discontinuity occurs when the function approaches infinity or negative infinity at a certain point.
To determine if a function has a discontinuity, you must first graph the function and look for any points where the function is undefined or where there is a sudden jump or break in the graph. You can also check the function's equation to see if there are any values that would make the function undefined.
Discontinuities are important in mathematics because they help us identify points where a function is not continuous. This can be useful in understanding the behavior of functions and in solving problems involving limits and derivatives.