Removable discontinuity

Definition

A removable discontinuity occurs at a point in a function where the limit exists, but the function is either not defined or defined differently. This type of discontinuity can be 'removed' by appropriately defining or redefining the function at that point.

5 Must Know Facts For Your Next Test

1. A removable discontinuity appears as a hole in the graph of a function.
2. It occurs when both left-hand and right-hand limits exist and are equal, but the function value at that point is either not defined or does not match the limit.
3. To remove the discontinuity, redefine the function so that it equals the limit at that point.
4. Removable discontinuities often occur in rational functions where factors cancel out from numerator and denominator.
5. Testing for removable discontinuities involves finding common factors in the numerator and denominator of a rational expression.

Review Questions

• What condition must be met for a discontinuity to be considered removable?
• How do you identify a removable discontinuity in a rational function?
• What steps are involved in 'removing' a discontinuity?

Related terms

Rational Function: A function expressed as the ratio of two polynomials.

Limit: The value that a function approaches as the input approaches some value.

Asymptote: A line that a graph approaches but never touches, often found in rational functions.