Consider the function $f(x) = 2 x - \cos(x) + 6$ on the interval $0\le x\le 1$. The Intermediate Value Theorem guarantees that for certain values of $k$ there is a number $c$ such that $f(c)=k$. In the case of the function above, what, exactly, does the intermediate value theorem say? To answer, fill in the following mathematical statements, giving an interval with non-zero length in each case.

For every $k$ in the interval $\le k \le$ ,
there is a $c$ in the interval $\le c \le$
such that $f(c) = k$.