Continuity of Polynomial Functions in their Domain

[Miike012]

The first hypothesis is that f is continuous on [a,b]...

Is there a more concise mathematical way of saying... "because the function f is a polynomial it is continuous in its domain."? Because I rather not write that on my test it looks sloppy and non professional...

 

[Mark44]

I don't see any problem with what you said. All polynomials are defined and continuous on the entire real line.

 

[Miike012]

I know but is there another way to state that using math symbols or something to make it more concise in like 2-5 words.

 

[Mark44]

This is all you need to say.
"...because the function f is a polynomial, it is defined and continuous [STRIKE]in its domain[/STRIKE] on the entire real line."

 

[LCKurtz]

Assuming you are using standard notation: "If p is a polynomial, then p ε C[a,b]".

 

[HallsofIvy]

Note, by the way, that Rolle's theorem also requires that the function be differentiable on some interval. Fortunately, it is also true that all polynomials are differentiable for all x.