# If f(c) = infinity and c is in [a,b]

• rsnd
In summary, if a function f is not continuous at c, where f(c) = infinity and c is in [a,b], it means that the function is not defined at c and therefore cannot be considered a continuous function from [a,b] to R. Additionally, if a function is continuous on a closed and bounded interval, it is also bounded, with both a superior and inferior bound. This means that there exists a parallel line to the horizontal axis at a point N such that f(x) <= N for every x in [a,b], and also a point N such that f(x) >= N for every x in [a,b].
rsnd
if f(c) = infinity and c is in [a,b]
is it equivalent to saying
f is not cont. at c ? because infinity is undefined?

Thanks
k.cv

It's NOT continuous.

SO it would also imply that if a function is cont. in a finite interval [a,b] then its bounded?

Yes, it has superior bound. There exist a number N such that f(x)<= N for every x in [a,b]. Geometricly speaking this means there exist a parallel line to the horizontal axis. And of course a inferior bound, the same for a number N such that f(x) >= N for every x in [a,b].

Last edited:
If a function f is continuous on a closed and bounded interval, then it is bounded. You implied "closed" when you said [a,b] but I want to make sure that is clear.

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rsnd said:
if f(c) = infinity and c is in [a,b]
is it equivalent to saying
f is not cont. at c ? because infinity is undefined?

Thanks
k.cv

If you're claiming f is a function from [a,b] to R, then f is not defined at c, and actually f therefore isn't a function, never mind a continuous one.

nice...I just invented the mean value theorom!

## 1. What does it mean if f(c) equals infinity?

When f(c) equals infinity, it means that the value of the function at point c is unbounded and has no finite limit. This can occur when the function has a vertical asymptote at c, meaning that the function approaches infinity as the input value approaches c.

## 2. Can a function have multiple values of infinity?

No, a function can only have one value of infinity. This is because infinity is not a number, but rather a concept of unboundedness. If a function has multiple vertical asymptotes, it may approach infinity at each of these points, but it is still considered to have one value of infinity.

## 3. Does f(c) equaling infinity mean that the function is undefined at c?

Not necessarily. While some functions may be undefined at points where they approach infinity, there are other cases where the function is well-defined and continuous at c, but still has a value of infinity. This is often seen in rational functions where the denominator approaches 0 at c.

## 4. How do you determine the behavior of a function when f(c) equals infinity?

The behavior of a function when f(c) equals infinity can be determined by analyzing the function's limits. If the limit of the function at c exists and is finite, then the function has a horizontal asymptote at that point. If the limit does not exist or is infinite, then the function has a vertical asymptote at c.

## 5. Can a function have a value of infinity at a finite point?

Yes, a function can have a value of infinity at a finite point. This occurs when the function has a vertical asymptote at that point. However, it is important to note that infinity is not a real number, so the function's output at that point is not considered a numerical value, but rather a concept of unboundedness.

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