התפקוד היומיומי השתפר אחרי הפיזיותרפיה.

Because the noun phrase is definite: the daily functioning.

In Hebrew, when a noun is definite with ה־ (the), any adjective that describes it also usually takes ה־.

• תפקוד = functioning
• התפקוד = the functioning
• יומיומי = daily
• היומיומי = the daily

So:

• התפקוד היומיומי = the daily functioning

This is normal Hebrew adjective agreement.

תפקוד most often means functioning or ability to function, especially in medical, psychological, or practical contexts.

In this sentence, התפקוד היומיומי means something like:

• daily functioning
• everyday functioning
• day-to-day functioning

It does not usually mean mathematical function, and here it is not really performance in the sense of a show or job evaluation.

יומיומי means daily, day-to-day, or everyday.

It comes from יום (day) and has a repeated pattern that gives the sense of something habitual or recurring. That is why it looks a bit like a doubled form.

Common translations:

• תפקוד יומיומי = daily functioning
• חיים יומיומיים = everyday life
• שגרה יומיומית = daily routine

So the repetition is just part of the word’s normal form.

השתפר means improved or got better.

It comes from the verb להשתפר, which is the usual verb for something improving on its own:

• המצב השתפר = the situation improved
• התפקוד השתפר = the functioning improved

This is different from לשפר:

• שיפרתי את המצב = I improved the situation

So:

• להשתפר = to improve / get better
• לשפר משהו = to improve something

In this sentence, the subject is התפקוד היומיומי, and it is the thing that improved, so השתפר is the correct choice.

It is past tense, 3rd person masculine singular.

Why masculine singular? Because the subject התפקוד is a masculine singular noun.

So:

• התפקוד השתפר = the functioning improved

If the subject were feminine singular, the verb would look different. For example:

• היכולת השתפרה = the ability improved

Because Hebrew past-tense verbs already include the idea of was/did inside the verb form.

So:

• השתפר already means improved / got better

Hebrew does not need an extra word like was in this sentence.

Compare:

• English: The functioning improved
• Hebrew: התפקוד השתפר

Very normal and natural.

אחרי means after.

So:

• אחרי הפיזיותרפיה = after the physiotherapy / after physiotherapy

A more formal alternative is לאחר:

• התפקוד היומיומי השתפר לאחר הפיזיותרפיה

Both are correct.
In general:

• אחרי = more common in everyday speech
• לאחר = often a bit more formal or written

Yes, both are possible, but they mean slightly different things.

• אחרי הפיזיותרפיה = after the physiotherapy
  This usually refers to a specific treatment or therapy course already known in context.

• אחרי פיזיותרפיה = after physiotherapy
  This sounds more general.

In your sentence, הפיזיותרפיה suggests a specific physiotherapy treatment the speaker and listener both know about.

Yes, basically.

In many varieties of English:

• physiotherapy and physical therapy refer to the same field

Hebrew normally uses פיזיותרפיה for that.

So depending on the English variety, the sentence could be translated as:

• Daily functioning improved after physiotherapy
• Daily functioning improved after physical therapy

Yes. Hebrew word order is fairly flexible.

The original sentence:

• התפקוד היומיומי השתפר אחרי הפיזיותרפיה

A very natural alternative is:

• אחרי הפיזיותרפיה, התפקוד היומיומי השתפר

Both mean the same thing. The difference is mostly about emphasis:

• starting with התפקוד היומיומי focuses first on what improved
• starting with אחרי הפיזיותרפיה focuses first on when/after what

A simple pronunciation guide is:

ha-taf-KUD ha-yo-myo-MI hish-ta-PER a-kha-REI ha-fi-zyo-te-RA-pya

A few notes:

• תפקוד = tafkud
• יומיומי = yomyomi
• השתפר = hishtaper
• אחרי = acharei
• פיזיותרפיה = fizyoterapya

The ch sound in אחרי is the throaty Hebrew sound, like in Bach for many speakers.

Not exactly.

התפקוד היומיומי means daily functioning or day-to-day functioning, especially in the sense of how well someone manages ordinary activities.

Routine would usually be something more like:

• שגרה = routine

So:

• התפקוד היומיומי השתפר = day-to-day functioning improved
• השגרה היומיומית השתפרה would be closer to the daily routine improved, though that is a less common idea

It breaks down like this:

• התפקוד היומיומי = the daily functioning
  
  • noun + adjective
• השתפר = improved
• אחרי הפיזיותרפיה = after the physiotherapy

So the structure is:

subject + verb + time/after phrase

In other words:

• [The daily functioning] [improved] [after the physiotherapy].

Usually it simply states that improvement happened in the past: improved / got better.

Whether it was gradual or sudden depends on context, not on the verb form itself.

So this sentence can fit either idea:

• the daily functioning improved over time after physiotherapy
• the daily functioning was better after physiotherapy

If you wanted to stress a process, Hebrew might add extra words, for example:

• התפקוד היומיומי הלך והשתפר אחרי הפיזיותרפיה = the daily functioning gradually improved after the physiotherapy