Level Unit 5-1 Mini Practice

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 a Removable Discontinuity?

Back

A Removable Discontinuity occurs when a function is not defined at a point, but the limit exists. It can be 'removed' by redefining the function at that point.

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 does it mean for a function to be Continuous at a point?

Back

A function is Continuous at a point if the limit as it approaches that point equals the function's value at that point.

Front

How can you identify a Jump Discontinuity on a graph?

Back

A Jump Discontinuity can be identified by a sudden 'jump' in the graph where the function's value changes abruptly without connecting the two points.

Front

How can you identify a Removable Discontinuity on a graph?

Back

A Removable Discontinuity can be identified by a hole in the graph where the function is not defined, but the limit exists.

Front

How can you identify an Infinite Discontinuity on a graph?

Back

An Infinite Discontinuity can be identified by a vertical asymptote in the graph where the function approaches infinity.

Front

What is the limit of a function at a point of Jump Discontinuity?

Back

The limit exists at a point of Jump Discontinuity, but it is not equal to the function's value at that point.

Front

What happens to the limits at a Removable Discontinuity?

Back

At a Removable Discontinuity, the left-hand limit and right-hand limit exist and are equal, but the function is not defined at that point.

Front

What is the significance of limits in understanding discontinuities?

Back

Limits help determine the behavior of a function at points of discontinuity, allowing us to classify the type of discontinuity present.