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

Identify the type of discontinuity: f(x) = 1/(x-2) at x=2.

Back

Infinite Discontinuity.

Front

Identify the type of discontinuity: f(x) = (x^2 - 4)/(x-2) at x=2.

Back

Removable Discontinuity.

Front

Identify the type of discontinuity: f(x) = { 1 for x < 0, 2 for x = 0, 3 for x > 0 } at x=0.

Back

Jump Discontinuity.

Front

What is the limit of f(x) = 1/(x-2) as x approaches 2?

Back

The limit is infinity.

Front

What is the limit of f(x) = (x^2 - 4)/(x-2) as x approaches 2?

Back

The limit is 4, but f(2) is undefined.

Front

What is the significance of identifying discontinuities in functions?

Back

Identifying discontinuities helps in understanding the behavior of functions, especially in calculus, where limits and continuity are crucial.