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trace back

1. To derive or originate from someone, something, or some place. The powerful corporation traces back nearly 200 years to a small manufacturing company in New York City. Investigators discovered that the drug money traced back to a US senator.
2. To discover the point of origin of someone or something by following a trail of information or series of events backward. In this usage, a noun or pronoun can be used between "trace" and "back." We were able to trace the assassination attempt back to a cartel in Mexico. Make sure you only pay in cash, as the police can trace back exactly where and when you use your card.

trace out

1. To trace, sketch, or delineate the outline of something. A noun or pronoun can be used between "trace" and "out." He traced out the directions to the cabin on the back of a napkin for me. I'm having a hard time visualizing what you mean. Why don't you trace it out on the whiteboard for us?
2. To develop, determine, or delineate something, such as a pattern or course of events, gradually over a period of time. A noun or pronoun can be used between "trace" and "out." The investigation traced out a pattern of corruption and abuse of power going all the way to the top of the administration. The film portrays the legendary actor's rise to fame, tracing it out from his humble beginnings to

trace back

v.
1. To ascertain the successive stages in the development or progress of something by reasoning backward from an effect to a cause: We traced our family history back 200 years. Skepticism as a philosophical movement can be traced back to Sextus Empiricus.
2. To derive from something or someone: The counterfeit drugs traced back to an American expatriate. Many English words trace back to Greek or Latin.

trace out

v.
1. To sketch or delineate something: I laid out the map and traced out the path to the park.
2. To delineate some pattern or development over time: The results traced out an interesting pattern of sudden fluctuations every three months. The biographer traced out the politician's rise to power.
3. To ascertain something by reconstructing a series of events: The police traced out the Internet cafe as the place where the virus was launched. The motive for the crime was so unusual that no one could trace it out.
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