Let   $S=\{x:\frac{x^3-9x^2+23x-15}{x^3-12x^2+44x-48}<0\};T=\{\frac{x}{y}:x,y\in \{1,2,3\}\}.$
Then which of the following statement is (are) true?

Every continuous function from S to T is differentiable.

There are 35 increasing functions from S to T.

There are less than 350 differential functions from S to T.

There are more than 350 continuous functions from S to T.