# Glossary

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Glossary Entries

Word(s)

Definition

continuity Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at every single point in an unbroken domain. CK-12
Continuous Continuity for a point exists when the left and right sided limits match the function evaluated at that point. For a function to be continuous, the function must be continuous at every single point in an unbroken domain. CK-12
Jump discontinuities Inverse functions are functions that 'undo' each other. Formally f(x) and g(x) are inverse functions if f(g(x))=g(f(x))=x. CK-12
limit A limit is the value that the output of a function approaches as the input of the function approaches a given value. CK-12
Removable discontinuities Removable discontinuities are also known as holes. They occur when factors can be algebraically canceled from rational functions. CK-12
Removable discontinuity Removable discontinuities are also known as holes. They occur when factors can be algebraically canceled from rational functions. CK-12
two-sided limit A two-sided limit is the value that a function approaches from both the left side and the right side. CK-12
Asymptotic A function is asymptotic to a given line if the given line is an asymptote of the function. CK-12
Horizontal Asymptote A horizontal asymptote is a horizontal line that indicates where a function flattens out as the independent variable gets very large or very small. A function may touch or pass through a horizontal asymptote. CK-12
Oblique Asymptote An oblique asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division. CK-12
Oblique Asymptotes An oblique asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division. CK-12
Piecewise Function A piecewise function is a function that pieces together two or more parts of other functions to create a new function. CK-12
Slant Asymptote A slant asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but will never reach. A slant asymptote exists when the numerator of the function is exactly one degree greater than the denominator. A slant asymptote may be found through long division. CK-12
Vertical Asymptote A vertical asymptote is a vertical line marking a specific value toward which the graph of a function may approach, but will never reach. CK-12
discontinuous A function is discontinuous if the function exhibits breaks or holes when graphed. CK-12
Polynomial Function A polynomial function is a function defined by an expression with at least one algebraic term. CK-12
rational function A rational function is any function that can be written as the ratio of two polynomial functions. CK-12
indeterminate In mathematics, an expression is indeterminate if it is not precisely defined. There are seven indeterminate forms: 00,0⋅∞,∞,∞−∞,00,∞0, and 1. CK-12

limit

A limit is the value that the output of a function approaches as the input of the function approaches a given value. CK-12
squeeze theorem The squeeze theorem (also known as the sandwich theorem) is used to find the limit of a function by bounding it between two other functions that each have the same limit. CK-12