Unlimited and Ungraded Practice Discontinuities

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit of a function at a certain point exist but are not equal, causing a 'jump' in the graph.

Front

What is an infinite discontinuity?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as it approaches a certain point, resulting in a vertical asymptote.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a certain point, but the limit exists at that point, allowing the function to be 'fixed' by redefining it.

Front

How can you identify a jump discontinuity on a graph?

Back

A jump discontinuity can be identified by observing a sudden 'jump' in the graph where the function value does not connect smoothly.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning the limit exists and equals the function value at every point in its domain.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions consist of distinct, separate values, while continuous functions have an unbroken range of values.

Front

What is the significance of the limit in determining continuity?

Back

The limit of a function at a point must equal the function's value at that point for the function to be continuous there.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity, indicating an infinite discontinuity.

Front

How do you find the locations of discontinuities in a function?

Back

To find discontinuities, analyze the function for points where it is not defined, where limits do not exist, or where left-hand and right-hand limits differ.

Front

What is the definition of a continuous function?

Back

A function f(x) is continuous at a point c if: 1) f(c) is defined, 2) lim (x -> c) f(x) exists, and 3) lim (x -> c) f(x) = f(c).