Level Unit 5-1 Mini Practice

Front

What is a discontinuity in a function?

Back

A discontinuity is a point at which a function is not continuous. This can occur due to a jump, hole, or vertical asymptote.

Front

What are the types of discontinuities?

Back

1. Infinite Discontinuity: Occurs when the function approaches infinity at a certain point. 2. Removable Discontinuity: A 'hole' in the graph where a limit exists but the function is not defined. 3. Jump Discontinuity: Occurs when the left-hand limit and right-hand limit at a point are not equal.

Front

Define Infinite Discontinuity.

Back

Infinite Discontinuity occurs when the function approaches infinity (positive or negative) as it approaches a certain x-value.

Front

Define Removable Discontinuity.

Back

Removable Discontinuity occurs at a point where the function is not defined, but the limit exists. It can often be 'fixed' by redefining the function at that point.

Front

Define Jump Discontinuity.

Back

Jump Discontinuity occurs when the left-hand limit and right-hand limit at a point are different, resulting in a 'jump' in the graph.

Front

What is the significance of identifying discontinuities in functions?

Back

Identifying discontinuities helps in understanding the behavior of functions, especially in calculus, where continuity is crucial for applying theorems.

Front

How do you determine if a function has a removable discontinuity?

Back

A function has a removable discontinuity if the limit exists at that point but the function is not defined or does not equal the limit.

Front

What is the difference between a removable and a jump discontinuity?

Back

A removable discontinuity can be 'fixed' by redefining the function at that point, while a jump discontinuity cannot be fixed as the limits from either side do not match.

Front

How can you identify an infinite discontinuity on a graph?

Back

An infinite discontinuity is identified on a graph where the function approaches infinity (upward or downward) as it approaches a certain x-value.

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 exists at that point, the function is defined at that point, and the function's value equals the limit.