The correct answer is option 1: 1 and 4 only.

A state function is a property that depends only on the current state of the system and not on how the system arrived at that state.

Option 1, q + w: q (heat) and w (work) are not state functions since they depend on the path taken to reach a certain state. The amount of heat and work exchanged between the system and its surroundings can vary depending on the specific path taken.

Option 2, q: As mentioned above, heat is not a state function.

Option 3, w: Work, like heat, also depends on the specific path taken and is not a state function.

Option 4, H - TS: H (enthalpy) and S (entropy) are state functions. Enthalpy is a measure of the total energy of a system and entropy is a measure of the system`s disorder. Since both H and S are state functions, their difference (H - TS) is also a state function.

In summary, only options 1 and 4 (q + w and H - TS) are state functions.