4. Some critics believe that the character Razumihin serves to increase a reader’s sympathy for Raskolnikov by helping to present him as a worthwhile man, even though he is a murderer. Cite incidents from the story to support this idea.

The presence of Razumihin helps us sympathize with Raskolnikov by showing him as his best friend without a doubt. A best friend won't talk bad about the other guy, in this case Raskolnikov, so whenever we see Razumuhin we try to understand Raskolnikov's situation, as if he was our friend.
A scene where we can create this empathy with Raskolnikov with Razumihin's help is when he feels really sick and has Razumihin taking care of him the whole time. In that time they spend together they talk a lot, and we realize about the way Raskolnikov reacts among other people.
Even though Razumihin doesn't know for sure that Raskolnikov is the one guilty of the murder, he suspects it and tries to show the goodness of Raskolnikov, hiding the possibility of him killing the pawnbroker.
In other scene, when Raskolnikov keeps feeling bad and his family (Dounia and Pulcheria) arrives, he acts really rude and the one responsible of controlling him and creating a better image of him by telling the women that Raskolnikov had been feeling really bad and had had some terrible events in the recent past is Razumihin, with a bit of personal interest because he's crazy for Dounia. It doesn't matter the reason, Razumihin shows us the better of Raskolnikov throughout the story.