Continuity of a function !

[meer]

Good Day!
the above is from munem calculus, chapter 2 , set 2.11 and topic is "change of sign property"
It says "polynomial function f is continuous on the interval [0, 1]"
my question is how do we know from above that function is continuous on the stated interval ?
Thank you.

 

[Harry_the_cat]

Any polynomial function is continuous.

 

[meer]

Any polynomial function is continuous.

THANK YOU

 

[JeffM]

The way this is written is a bit confusing. You need to be aware that it is a general theorem about polynomials

Every polynomial is continuous and infinitely differentiable in
[imath](- \infty, \ \infty)[/imath].

So steps in the reasoning based on this general theorem have been left implicit

[math]\text {All polynomials are continuous in } (-\infty, \infty) \implies\\ \text {The polynomial } f(x) \text { is continuous in any interval} \implies \\ f(x) \text { is continuous in } [0, 1]. [/math]
It would be clearer English to write

As a polynomial, f(x) is continuous in [0, 1]

 

[Steven G]

I agree with the others.
You can't just say that f(x) is continuous on [0,1].
It has been next to impossible to get my students to explain why f(x) is continuous on an interval.
As JeffM stated, f(x) is a polynomial and all polynomials are continuous on any interval. Hence f(x) is continuous on [0,1]