Discontinuities in Functions Start

Front

What is the limit of a polynomial function as x approaches c?

Back

Front

Does the graph of a polynomial function contain a break?

Back

Never. Polynomial functions are continuous everywhere.

Front

What is the limit of a rational function as x approaches c?

Back

Front

What is a discontinuity in a function?

Back

A point where a function is not continuous, meaning it does not have a limit or the limit does not equal the function's value.

Front

What are the types of discontinuities?

Back

1. Removable Discontinuity 2. Jump Discontinuity 3. Infinite Discontinuity

Front

What is a removable discontinuity?

Back

A point where a function is not defined, but can be made continuous by redefining the function at that point.

Front

What is a jump discontinuity?

Back

A point where the left-hand limit and right-hand limit exist but are not equal.

Front

What is an infinite discontinuity?

Back

A point where the function approaches infinity or negative infinity as x approaches a certain value.

Front

How can you identify a removable discontinuity in a rational function?

Back

If the function can be simplified and the factor causing the discontinuity cancels out.

Front

What is the Intermediate Value Theorem?

Back

If a function is continuous on [a, b], then it takes every value between f(a) and f(b).