word-usage
I understand that the intransitive use of the verb "focus " is often followed by the preposition "on," but is it OK to say "focus at" instead of "focus on?" If not, why?
Below is one of the definitions of the verb I found in my dictionary.
to direct your attention or effort at something specific.
Yes, you understand correctly.
Steven approved of the whole affair. Intransitive, takes indirect object, so "of" is correct.
The directors quickly approved the new deal. Transitive, takes direct object, adding "of" would change it to intransitive, which is not what you meant.
At first glance, You always dress in a black suit looks pretty equivalent to You are always dressed in a black suit, with the apparent meaning being "You always wear a black suit". A number of people commented that they are the same. In fact, both constructions are in common usage. You might even hear cases of the constructions being used interchangeably. However, they are actually different, and when used properly, they are used differently, and with a different nuance in meaning.
The main source of confusion is in viewing the difference between the sentences as relating to different tenses of the verb "dress". In fact, there is discussion in the comments that "are dressed" is simply passive construction. I'll explain how and why the sentences are different, and how the usage is different when speakers are not being sloppy with the language. [1]
The gist of the difference stems from this: you dress... describes a habit, you are dressed... describes a present example or observation of the habit.
Tense
Lets focus first on tense and consider a simplified example:
You always dress in a black suit
Simple present "dress" is the verb, and this describes your habit. It would be said by someone familiar enough with your routine to know that it's what you always do. It could refer to what you're currently wearing, but it could also be said in a context that doesn't involve that person actually seeing you, and it could refer to any time frame.
For example, you could be having a telephone conversation with the person discussing what you should wear at an upcoming event.
You: "What should I wear?"
Other person: "You always dress in a black suit."
That's a comment about your habit. The meaning would depend on the context of the discussion and the intonation of the words. It could be a suggestion to wear what you usually wear, or it could be a suggestion to wear something other than what you usually wear.
Notice that this construction has no inherent positive or negative connotation. In addition to the positive and negative examples above, it can be used with no value connotation at all, simply a statement of fact.
You are always dressed in a black suit
As similar as this sentence seems, it is actually a different beast. I'll break it down. Consider this sentence:
You are tall.
"Tall" is an adjective describing "you". "Are" is the verb. Now replace "tall":
You are [dressed in a black suit].
In this construction, "dressed" is not the past tense of the verb "dress", it is an adjective, part of an adjective phrase that describes "you". By coincidence the Macmillan Dictionary definition of "dressed" as an adjective uses this as an example: "She was dressed in a black suit." What are the odds of that coincidence?
So "dressed" does not contribute a tense, it is not a past participle verb, and it is not part of an "are dressed" passive construction. The only verb in the sentence is "are", and as in the discussion under Tense, it explicitly describes something in the present. The present is one example, or an observation of one example, of the habit.
"Always" indicates that it is something recurring and routine, as in "You always say that". "Always" in combination with "are" refers to a recurring pattern or series of then-present events. These are examples or observations of the habit.
This is the perspective of an observer. The observer sees a collection of then-present examples, which for the observer, is a pattern of observations. This construction is a generic reference to the observations of the habit rather than the habit, itself.
It would most likely be said by someone observing you and commenting on your present attire. It would typically mean:
Every time I see you, you are wearing a black suit.
It is a reference to their observations of you rather than to what you wear when they don't see you.
This construction is different from simple present in terms of the usual positive/negative connotations of its use. It is rarely used with a positive connotation. It can be used in a neutral way, but it tends to be used with a negative (or sarcastic) connotation.
Going back to the telephone discussion of attire for a future event, this construction could also be used there, but in a slightly different context. It would also reflect the perspective of the observer more than your habit. The two constructions:
You: "I think I'll wear a black suit."
Other person: "You always dress in a black suit."
This is a reference to your habit and a suggestion to change it for this event.
You: "I think I'll wear a black suit."
Other person: "You are always dressed in a black suit."
The perspective of this comment is that a black suit is what other people always see you in and a suggestion to let them see you in something different.
[1] Many thanks to Ben Kovitz for identifying the language principles underlying the "why".
Best Answer
To focus on something is a collocation, like to direct at something; although the former is the only one possible (according to the Oxford Collocation dictionary, at least), whereas the verb to direct may collocate with different prepositions (at, into, to, toward(s), and a few others).
Why? Because it's a set phrase, like to look forward to, to be afraid of, to be angry with and so on.
To deside whether to focus may be used with "at" is impossible without a context