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Robertson will remain with the organization after being claimed off waivers earlier this offseason from the Angels. The 30-year-old posted a .280/.299/.307 line in 75 at-bats over 37 games last season and also hit .271/.333/.333 in 177 at-bats over 70 games for the Rangers in 2014.
Rasmussen, 26, was one of three pitchers acquired at the non-waiver Trade Deadline from the Blue Jays for Mark Lowe. The former UCLA hurler was 2-1 with a 10.67 ERA in 19 games with Seattle, allowing 25 hits and a 2.30 WHIP in 14 1/3 innings.
In 30 Major League games over the past two seasons with Seattle and Toronto, Rasmussen posted a 7.09 ERA in 26 2/3 innings with 30 strikeouts and 15 walks.
The other two pitchers acquired in the Lowe trade -- left-handers Jake Brentz and Nick Wells -- are still in the Mariners' organization after finishing the year with Class A Everett.
Brentz, 21, went 1-1 with a 3.86 ERA in five games (four starts) with the AquaSox, while the 19-year-old Wells was 1-0 with a 1.00 ERA in four games (three starts).
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB, read his Mariners Musings blog, and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.