Etymology
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cast-off (adj.)

1709, "put aside, rejected," from verbal phrase cast off "discard, reject" (c. 1400), from cast (v.) + off (adv.). From 1741 as a noun, "person or thing abandoned as worthless or useless." Related" Cast-offs.

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lead-off (n.)
"commencement, beginning," 1879, from verbal phrase (attested from 1806); see lead (v.1) + off (adv.).
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well-off (adj.)
1733, "comfortable," from well (adv.) + off. Meaning "prosperous, not poor" is recorded from 1849.
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trade-off (n.)
also tradeoff, "sacrifice of one benefit for another," 1959, from verbal phrase to trade off; see trade (v.) + off (adv.).
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off-road (adj.)

"used, meant to be used, or taking place away from roads," 1949, from off- (adj.) (see off (prep.)) + road.

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push-off (n.)

"act of pushing off" (a boat, from the land), 1902, from the verbal phrase; see push (v.) + off (adv.).

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tip-off (n.)
1901 in reference to information, from tip (v.2) + off (adv.). From 1924 in basketball, from tip (v.3).
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face-off (n.)
also faceoff, 1886 in sports (hockey, etc., originally lacrosse), from verbal phrase in a sports sense, attested from 1867 (see face (v.) + off (adv.)); the off perhaps is based on stand-off or similar constructions.
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lift-off (adj.)
"removable by lifting," 1907, from the verbal phrase, from lift (v.) + off (adv.)
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off-base (adv.)

"unawares," by 1936, American English, from off (adv.) + base (n.); a figurative extension from baseball sense of a runner being "not in the right position" (1882) and vulnerable to being picked off.

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