What field of study are you asking about? I'm in the biosciences field and this is a regular thing that comes up. Professors generally will tell you if they can't write you a reference. It helps to ask if they want a current CV. In my field, it's easier if you have undergrad lab experience and that prof writes you one of your references. I've found in biosciences that the reference letters for graduate school are a simple requirement - the PI with whom you will work is often more interested in talking to you directly and whoever supervised your research project.
Good luck.
Oh, and if it's in and of the non-applied sciences, think wisely whether you actually want (and need) to do graduate school.
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