Suppose the function $f$ is continuous on the closed interval $\lbrack 1, 2 \rbrack$, $f(1) = 5$, and $f(2) = 9$. Then, from the Intermediate Value Theorem we can conclude that...(select all that apply)

A. $f(1.5) = 7$.
B. there must exist at least one number $c$ between $1$ and $2$ such that $f(c) = 10$.
C. for any value of $y$ between $5$ and $9$, there exists at least one number $c$ between $1$ and $2$ such that $f(c) = y$.
D. there must exist at least one number $c$ between $1$ and $2$ such that $f(c) = 7.5$.