Select the appropriate preposition to fill in the blank in the following…

Certain English adjectives combine with one fixed preposition by convention, and the preposition often depends on which sense of the adjective is being used — a literal physical sense versus a figurative sense of unwillingness or lack of response. These are collocations that must be learned rather than derived from general prepositional meaning.

1. The adjective here is "deaf", and the clause describes his response to "my request for help" — this is the figurative sense of deaf, meaning refusing to listen to or heed something, not the literal sense of being unable to hear.

2. In this figurative sense, deaf takes a single fixed preposition: "deaf to" (as in "deaf to advice" or "deaf to pleas"), so the correct completion is "He is deaf to my request for help."

3. "Of" is eliminated because it pairs with verbs and adjectives of awareness or origin, such as "aware of" or "hear of", not with the figurative sense of deaf.

4. "For" is eliminated because it pairs with purpose, duration, or benefit, such as "wait for" or "responsible for", not with the figurative sense of deaf.

5. "At" is eliminated because it pairs with a point of focus or the target of a reaction, such as "look at" or "surprised at", not with the figurative sense of deaf.

This matches the same fixed pattern seen in the related idiom "turn a deaf ear to [something]", confirming "to" as the consistent, non-exceptional choice for this figurative use of deaf.

Therefore, the correct preposition is "to".