Continuous Function
Definition
A continuous function is one that has no breaks, holes, or jumps in its graph. It can be drawn without lifting the pen from the paper.
Analogy
Think of a continuous function as a smooth roller coaster ride with no sudden drops or gaps. You can smoothly travel along the track without any interruptions or moments where you are not connected to the track.
Related terms
Discontinuous Function: A discontinuous function has one or more breaks, holes, or jumps in its graph. It cannot be drawn without lifting the pen from the paper.
Intermediate Value Theorem: This theorem states that if a continuous function takes on two different values at two points within an interval, then it must also take on every value between those two points within that interval.
Limit: The limit of a function represents what value it approaches as the input gets arbitrarily close to a certain point. It helps determine behavior near points of discontinuity and infinity.
"Continuous Function" appears in:
Study guides (1)
Practice Questions (2)
- If f(x) is a continuous function defined over the interval [a,b], what does the integral \int_{a}^{b} f(x) ,dx represent?
- For a continuous function f(x) over an interval [a, b], which of the following statements is true about the average value of f(x)?
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