how do you know if f is continuous ?

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how do you know if f is continuous ?

Here are some links that might be useful to you:

https://www.wikihow.com/Check-if-a-Function-Is-Continuous

https://www.wikihow.com/Check-if-a-Function-Is-Continuous
How to Check if a Function Is Continuous: Point or Interval – wikiHow
27 sept. 2023Things You Should Know. This tutorial uses a general rule (tracing) and limits to check for continuity. Look for point, jump, and asymptotic discontinuities in your function. For a point, take the limit of f (x) = f (c) for x approaches c. For a closed interval, you’ll need to take two limits, one for each end of the interval. Method 1.

https://www.dummies.com/article/academics-the-arts/math/pre-calculus/how-to-determine-whether-a-function-is-continuous-167760

https://www.dummies.com/article/academics-the-arts/math/pre-calculus/how-to-determine-whether-a-function-is-continuous-167760
How to Determine Whether a Function Is Continuous or … – dummies
A graph for a function that’s smooth without any holes, jumps, or asymptotes is called continuous. Your pre-calculus teacher will tell you that three things have to be true for a function to be continuous at some value c in its domain: . f(c) must be defined. The function must exist at an x value (c), which means you can’t have a hole in the function (such as a 0 in the denominator).

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

https://www.mathsisfun.com / calculus / continuity.html
Continuous Functions – Math is Fun
A function f is continuous when, for every value c in its Domain: f (c) is defined, and. lim x→c f (x) = f (c) the limit of f (x) as x approaches c equals f (c) . The limit says: as x gets closer and closer to c. then f (x) gets closer and closer to f (c) And we have to check from both directions:

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/02:_Limits/2.04:_Continuity

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/02:_Limits/2.04:_Continuity
2.4: Continuity – Mathematics LibreTexts
18 nov. 2023Figure 2.4.1 2.4. 1: The function f(x) f ( x) is not continuous at a a because f(a) f ( a) is undefined. However, as we see in Figure 2.4.2 2.4. 2, this condition alone is insufficient to guarantee continuity at the point a a. Although f(a) f ( a) is defined, the function has a gap at a a.

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
About. Transcript. Discover how to determine if a function is continuous on all real numbers by examining two examples: eˣ and √x. Generally, common functions exhibit continuity within their domain. Explore the concept of continuity, including asymptotic and jump discontinuities, and learn how to identify functions in various …

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/continuity-over-an-interval

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-12/v/continuity-over-an-interval
Continuity over an interval (video) | Khan Academy
Google Classroom. AboutAbout this video. Transcript. A function ƒ is continuous over the open interval (a,b) if and only if it’s continuous on every point in (a,b). ƒ is continuous over the closed interval [a,b] if and only if it’s continuous on (a,b), the right-sided limit of ƒ at x=a is ƒ (a) and the left-sided limit of ƒ at x=b is (b).

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
A function that remains level for an interval and then jumps instantaneously to a higher value is called a stepwise function. This function is an example. A function that has any hole or break in ….

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
Continuity over an Interval. Now that we have explored the concept of continuity at a point, we extend that idea to continuity over an interval.As we develop this idea for different types of intervals, it may be useful to keep in mind the intuitive idea that a function is continuous over an interval if we can use a pencil to trace the function between any two points in the interval without …

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/v/continuity-at-a-point

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-11/v/continuity-at-a-point
Continuity at a point (video) | Khan Academy
I know this is a silly question; more of a joke honestly. And to clarify, I know the answer. But if the formal definition of whether a function is continuous is lim_x->c f(c) = f(c), and you have a graph with a jump discontinuity at both ends of a point… Example f(x)={x if 0 < x < 2, 5 – x if 2 < x < 4}

https://courses.lumenlearning.com/calculus1/chapter/continuity-over-an-interval

https://courses.lumenlearning.com/calculus1/chapter/continuity-over-an-interval
Continuity Over an Interval | Calculus I – Lumen Learning
A function f (x) f ( x) is said to be continuous from the left at a a if lim x→a−f (x) = f (a) lim x → a − f ( x) = f ( a). A function is continuous over an open interval if it is continuous at every point in the interval. A function f (x) f ( x) is continuous over a closed interval of the form [a,b] [ a, b] if it is continuous at every …
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