Quarterback Kurtis Rourke was back at the San Francisco 49ers’ practice facility Friday, one day after he was taken to the hospital as a precaution following a big hit to his chest.

The 49ers did not have an update on the specific injury, characterizing it only as a rib issue. Coach Kyle Shanahan said Thursday evening that X-rays taken at Levi’s Stadium did not show a fracture but that because Rourke was having difficulty breathing regularly, the team took him to a local hospital. He was discharged Thursday night and was observed at the team facility Friday.

Rourke appeared to get hurt on a draw play at the goal line in the second quarter. He didn’t leave the field then. But after the 49ers scored two plays later, he went into the blue medical tent on the sideline, then walked slowly to the locker room.

“They said that it didn’t seem broken on the first X-ray,” Shanahan said after the game. “Then at halftime, they said they wanted to take him to the hospital just because he was struggling with some breath stuff. … When you don’t see something on X-ray, and someone’s struggling with something, then you’ve just got to go cover your bases and look for more.”

Rourke, who essentially redshirted his rookie season last year as he rehabilitated from a college ACL injury, looked good in roughly a quarter and a half of play, completing 12 of 14 passes for 101 yards against the Tennessee Titans’ first-string defense. That included the biggest offensive highlight of the game, a 32-yard pass to rookie receiver De’Zhaun Stribling.

The 49ers’ top two quarterbacks, Brock Purdy and Mac Jones, didn’t suit up, leaving Adrian Martinez as the only quarterback after Rourke left the field. If Martinez had gotten hurt, Shanahan would have sent in tight end Brayden Willis to play quarterback.

Shanahan said the team might have to add another quarterback if Rourke is out long-term, though he also noted that doing so would be difficult given all the other injuries on the 90-man roster.

“We still have three (quarterbacks) in here, so it’s not a necessity,” he said. “With other guys on the roster, it might be hard to carry five.”

Cornerbacks Jack Jones (hand) and safety Marques Sigle (oblique) were also hurt Thursday, while cornerback Nate Hobbs suffered a groin injury in Tuesday’s joint practice and “will miss a few weeks,” Shanahan said. Because of that, the team worked out a trio of cornerbacks on Friday: Bryce Hall, Corey Mayfield and Troy Pride.