Assuming you are an at will employee, it is not illegal for your employer to change your job description. If you feel you are underpaid, you may want to look for another job, especially if you feel your employer will terminate you merely for asking for a raise.
Not illegal unless you have some kind of contract that sets your duties. If you have a union, you should discuss this with your union representative.
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It is perfectly legal for an at will employer to work you at as many positions as it wishes, and to label those positions with whatever title it wants. It has no duty to inform prospective employers who ask about what you did, and it would be somewhat unusual for that to occur.
You will have to demonstrate your knowledge and experience in the roles you have held through other means. Good luck to you in your job search.
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I agree with the other attorneys' responses to this answer. If you are a member of a union you may want to check with the union to see if this is a collective bargaining violation. Best of luck.
As the other attorneys have said, you may want to start looking for another job. If you are prepared to do that, and are prepared to maybe get fired, then perhaps asking for that raise is not a bad idea. You could approach your supervisor/manager and logically and calmly lay out your request and specific duties you perform as the inventory control manager, etc., and see what happens. This could have positive effects - or negative - but it might be worth the shot.
I agree with my colleagues...but even if you are sure that any request for a raise won't go over well, have you considered just asking for an official title change to Inventory Control Manager, without any request for a matching raise? Many employers don't care what employees call themselves as long as the work gets done, and if you can get your title changed, that might help with the job search, since potential future employers will have a clearer idea of what your skills are. Good luck.