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Suppose that a function $f$ is continuous on the interval $[0,1]$.

Which of the following facts are TRUE?

Select ALL that apply.

$f$ achieves a maximum on the interval $[0,1]$.

$f$ is uniformly continuous on the interval $[0,1]$.

$f$ can be extended to a continuous function on all of $\mathbb{R}$.

$f(x)=0$ for some $x \in [0,1]$.