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 infinite behavior.

Front

What are the types of discontinuities?

Back

1. Infinite Discontinuity: Occurs when the function approaches infinity at a 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

How do you identify a removable discontinuity?

Back

A removable discontinuity can be identified if the limit exists at a point but the function is not defined at that point.

Front

How do you identify an infinite discontinuity?

Back

An infinite discontinuity is identified when the function approaches infinity as it approaches a certain x-value.

Front

How do you identify a jump discontinuity?

Back

A jump discontinuity is identified when the left-hand limit and right-hand limit at a point are not equal.

Front

What is the significance of discontinuities in calculus?

Back

Discontinuities are significant because they indicate points where a function may not behave predictably, affecting limits, derivatives, and integrals.

Front

Provide an example of a function with a removable discontinuity.

Back

f(x) = (x^2 - 4)/(x - 2) has a removable discontinuity at x = 2.