Etymology
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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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off-hand (adv.)

also offhand, 1690s, "at once, straightway," from off (prep.) + hand (n.). Probably originally in reference to shooting "from the hand," without a rest or support. Hence, of speech or action, "without deliberation, unpremeditated" (1719). Related: Off-handed; off-handedly.

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off-limits (adj.)

"forbidden, outside the limits within which a particular group or person must remain," by 1881, U.S. military academies jargon, from off (prep.) + limit (n.). Earlier (1857) it was applied to cadets, etc., who were in violation of the limitations on their movement and behavior.

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off-line (adj.)

1926, of railroads, "not done on a railway;" 1950, in computing, "not controlled by or connected to a computer or network;" from off (prep.) + line (n.).

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off-season (n.)

1848, "a period when business is down," from off- (adj.) (see off (prep.)) + season (n.).

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