Continuity

Continuity

Assessment

Flashcard

Mathematics

11th - 12th Grade

Practice Problem

Hard

CCSS
HSF-IF.C.7D, HSF.IF.A.2

Standards-aligned

Created by

Wayground Content

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14 questions

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1.

FLASHCARD QUESTION

Front

What is continuity in mathematics?

Back

Continuity refers to a property of a function where it is uninterrupted or unbroken at a point or over an interval. A function is continuous at a point if the limit as it approaches that point equals the function's value at that point.

Tags

CCSS.HSF-IF.C.7D

2.

FLASHCARD QUESTION

Front

What does it mean for a function to be continuous at a point x = a?

Back

A function f(x) is continuous at x = a if: 1) f(a) is defined, 2) the limit of f(x) as x approaches a exists, and 3) the limit equals f(a).

Tags

CCSS.HSF.IF.A.2

3.

FLASHCARD QUESTION

Front

What is removable discontinuity?

Back

Removable discontinuity occurs at a point where a function is not defined or has a hole, but can be made continuous by defining or redefining the function at that point.

Tags

CCSS.HSF-IF.C.7D

4.

FLASHCARD QUESTION

Front

What is jump discontinuity?

Back

Jump discontinuity occurs when the left-hand limit and right-hand limit at a point exist but are not equal, causing a 'jump' in the function's value.

Tags

CCSS.HSF-IF.C.7D

5.

FLASHCARD QUESTION

Front

What is infinite discontinuity?

Back

Infinite discontinuity occurs when the function approaches infinity or negative infinity as it approaches a certain point, resulting in a vertical asymptote.

Tags

CCSS.HSF-IF.C.7D

6.

FLASHCARD QUESTION

Front

What is the definition of a continuous function over an interval?

Back

A function is continuous over an interval if it is continuous at every point within that interval.

7.

FLASHCARD QUESTION

Front

Provide an example of a function that is continuous everywhere.

Back

The function f(x) = x^2 is continuous everywhere on the real number line.

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