Q. Can my parents claim me if I am 19 years old, working full time, live at home but not yet in college?
A. No.
There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" [QR] in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.
The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
You cannot be a QC because you are over 18 and not a full time student. You cannot be a QR because your income for the year was more than $4700 (I assume because you're "working full time").
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
