what functions are continuous ?

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https://en.wikipedia.org/wiki/Continuous_function

https://en.wikipedia.org/wiki/Continuous_function
Continuous function – Wikipedia
In mathematics, a continuous function is a function such that a continuous variation (that is, a change without jump) of the argument induces a continuous variation of the value of the function. This means there are no abrupt changes in value, known as discontinuities.

https://www.mathsisfun.com/calculus/continuity.html

https://www.mathsisfun.com/calculus/continuity.html
Continuous Functions – Math is Fun
Here is a continuous function: Examples So what is not continuous (also called discontinuous) ? Look out for holes, jumps or vertical asymptotes (where the function heads up/down towards infinity). Not Continuous (hole) Not Continuous (jump) Not Continuous (vertical asymptote) Try these different so you get the idea:

https://www.cuemath.com / calculus / continuous-function

https://www.cuemath.com / calculus / continuous-function
Continuous Function – Definition, Examples | Continuity – Cuemath
A continuous function, as its name suggests, is a function whose graph is continuous without any breaks or jumps. i.e., if we are able to draw the curve (graph) of a function without even lifting the pencil, then we say that the function is continuous.

https://openstax.org/books/calculus-volume-1/pages/2-4-continuity

https://openstax.org/books/calculus-volume-1/pages/2-4-continuity
2.4 Continuity – Calculus Volume 1 | OpenStax
A function f ( x) is continuous at a point a if and only if the following three conditions are satisfied: f ( a) is defined lim x → a f ( x) exists

https://brilliant.org/wiki/continuous-functions

https://brilliant.org/wiki/continuous-functions
Continuous Functions | Brilliant Math & Science Wiki
In calculus, a continuous function is a real-valued function whose graph does not have any breaks or holes. Continuity lays the foundational groundwork for the intermediate value theorem and extreme value theorem.

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/functions-continuous-on-all-numbers

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/functions-continuous-on-all-numbers
Functions continuous on all real numbers (video) | Khan Academy
Is it a constant? • ( 22 votes) Jesse M 7 years ago e stands for Euler’s constant, which is about 2.718. It’s a bit like pi: they’re both specific symbols to refer to an irrational constant. e is closely tied to the natural logarithm, which is written as ln (x). In general, log (x) involves a log of base ten, so log (x)=y means that 10^y=x.

https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity

https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity
Limits and continuity | Calculus 1 | Math | Khan Academy
Unit 1 Limits and continuity. Unit 2 Derivatives: definition and basic rules. Unit 3 Derivatives: chain rule and other advanced topics. Unit 4 Applications of derivatives. Unit 5 Analyzing functions. Unit 6 Integrals. Unit 7 Differential equations. Unit 8 Applications of integrals. Course challenge.

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/12:_Introduction_to_Calculus/12.03:_Continuity

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/12:_Introduction_to_Calculus/12.03:_Continuity
12.3: Continuity – Mathematics LibreTexts
Example 12.3.3: Determining Whether a Rational Function is Continuous at a Given Number. Determine whether the function f(x) = x2 − 25 x − 5 is continuous at x = 5. To determine if the function f is continuous at x = 5, we will determine if the three conditions of continuity are satisfied at x = 5.

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_2_Limits/2.6:_Continuity

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_2_Limits/2.6:_Continuity
2.6: Continuity – Mathematics LibreTexts
2.6: Continuity. Summary: For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite.

https://people.math.harvard.edu/~knill/teaching/math1a2020/handouts/lecture04.pdf

https://people.math.harvard.edu/~knill/teaching/math1a2020/handouts/lecture04.pdf
PDF Unit 4: Continuity – Harvard University
Intuitively, a function is continuous if you can draw the graph of the function without lifting the pencil. Continuity means that small changes in x results in small changes of f(x). 4.3. Example. Any polynomial like x3 or trig functions like cos(x); sin(x); exp(x) are continuous everywhere. Also the sum and product of such is . lesoutrali bot