# Thread: Continuous functions

1. ## Continuous functions

Hi,

I have a lot of ambiguity about understanding the concept of continuous functions.The general explanation given for a continuous function is that the point moves smoothly without a break.Then is a constant function continuous?

let us assume,f(x)=2*X then df/dx =2 is this continuous?

can anyone explain this to me?
-swetha

2. ## Re: Continuous functions

A function is continuous if the function is defined at every point, and if the limit of the function at that point exists and is equal to the function value.

4. ## Re: Continuous functions

Yes, every constant function is continuous. In fact, every polynomial is continuous.

5. ## Re: Continuous functions

Thankyou for your answers.so,if f(x)= constant then y=df/dx=0 =>y(x)=0 which represents the real-line.I think y is also continuous. am i right?
-swetha

6. ## Re: Continuous functions

Originally Posted by swethapradeepp
Thankyou for your answers.so,if f(x)= constant then y=df/dx=0 =>y(x)=0 which represents the real-line.I think y is also continuous. am i right?
-swetha
Yes, since a constant function is a polynomial (of degree 0) and all polynomials are continuous.

Or to use the more precise definition, the constant function is defined at every point (and is equal to that constant value), and at every point, the limit is equal to the function (constant) value at that point.