Continuity
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
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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 and has no breaks, jumps, or holes in its graph.
2.
FLASHCARD QUESTION
Front
What does it mean for a function to be continuous at a point x = a?
Back
A function is continuous at x = a if the following three conditions are met: 1) f(a) is defined, 2) the limit of f(x) as x approaches a exists, and 3) the limit equals f(a).
3.
FLASHCARD QUESTION
Front
What is a polynomial function?
Back
A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.
4.
FLASHCARD QUESTION
Front
Is a polynomial function continuous everywhere?
Back
TRUE. Polynomial functions are continuous for all real numbers.
5.
FLASHCARD QUESTION
Front
What is removable discontinuity?
Back
Removable discontinuity occurs at a point where a function is not defined, but can be made continuous by defining or redefining the function at that point.
6.
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.
7.
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 graph.
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