Weierstrass Approximation Theorem

Question

Does it matter what the interval is in the Weierstrass Approximation Theorem? Is it possible that the interval be any possible numbers within the function f(x)? How much the interval matter?

Answer 1

The interval must be closed and bounded, so of the form $[a,b]$ for some $a, b \in \mathbb{R}$. But any $a$ and $b$ will work, if $f$ is defined and continuous on the interval $[a,b]$.

Answer 2

If the interval becomes larger, the approximation polynomial has in general a much higher degree.