Discontinuity
Definition
A discontinuity occurs when there is a break or jump in the graph of a function, meaning that the function is not continuous at that point.
Analogy
Imagine you are walking along a path and suddenly there is a big gap in the ground. You can't continue walking smoothly because there is an interruption in the path, just like how a function can't be continuous if there is a break or jump in its graph.
Related terms
Asymptote: A line that a graph approaches but never touches.
Removable Discontinuity: A type of discontinuity where the function has a hole at that point, but it can be filled to make the function continuous.
Jump Discontinuity: A type of discontinuity where the function has two different values on either side of the point, causing a vertical jump in its graph.
"Discontinuity" appears in:
Additional resources (1)
Practice Questions (8)
What type of discontinuity does the function have if the left and right-handed limits are not equal?
Which type of discontinuity occurs when a function has a "hole" at a certain point?
If a function approaches closer and closer to a certain value but never reaches it, what type of discontinuity does it have?
What type of discontinuity does a function have if it is not defined at a particular point?
What type of discontinuity does the function f(x) = 1/x have at x = 0?
If the left-handed limit of a function at a certain point is 5 and the right-handed limit is 3, what type of discontinuity does the function have at that point?
What are the steps to figure out whether a function has a discontinuity?
For what value is there a discontinuity on the function f(x)= (x^2-9)/(3x^2+2x-8)?
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