Sathish, examples will only take you so far!  You have some examples, so the next stage is where you test yourself to see  how well you've understood them.  Here's a little exercise for you.

Match the sentences ( 1 - 6) with the functions (A - F) :

1     Would you like to come for dinner tomorrow night?

2    I'm sorry to hear that your mother is ill.

3    Could you open the window, please?

4    Excuse me, but the shower in my room isn't working.

5    I'm afraid I won't be able to come to your party.

6    Well done!  You made a wonderful speech.

A    Making a request

B    Showing sympathy

C    Inviting

D    Congratulating

E    Complaining

F    Apologising

 My suggestions:

 2. He lost his job? What a shame! - Sympathy

 3. You could have fed the cat. - Criticism

 4. I must stop eating junk food. - Resolution / Decision

 5. Could you possibly do this on your way back? - Request (Polite/Formal)

 6. Let's go for a walk. - Request

 7.  How annoying! - Displeasure

 8. We're sorry about the delay in processing your request. - Apologies

 9. Please wear your seatbelts  seat belts - Instruction

Thanks Suki,

In the order of sentences

Inviting

Showing Sympathy

Making a request

Complaining

Apologizing

Congratulating

However, these sentences feel much easier than what I had posted. This is being difficult only with certain sentences, not all of them in general. Was hoping to deal with such sentences.