On Sunday, President-elect Donald J. Trump looked directly into the camera on CBS’ “60 Minutes” and urged U.S. citizens to end a recent swell of violent incidents based on race and culture. “Stop it,” he said.

On Monday, “Daily Show” host Trevor Noah put his own twist on the remarks: “And frisk it,” he added.

The joke was funny – and, uttered by a host of mixed parentage who hails from South Africa, particularly knowing. Tuesday night on “The Daily Show,” the Comedy Central institution he inherited from Jon Stewart in 2015, Noah drew very telling comparisons between Trump’s behavior and that of Jacob Zuma, the South African president who has tangled with a long list of corruption and racketeering charges. At the end of the segment, Noah wondered aloud if he’d be able to even consider saying such things once Trump took up the reins of the Oval Office.

“It’s a bizarre new world,” said Steve Bodow, the late-night program’s executive producer. “There’s going to be a lot for us to say and do.”

Noah could prove to be one to watch as the nation’s late-night comedians figure out how to tackle a polarizing U.S. president who has said during campaign speeches that he might like to “open up” libel laws, while also appealing to two different chunks of audience, one that supported Trump’s election and another that is vehemently opposed to it.

“Some are probably audience members of ours,” said Bodow, speaking of Trump supporters. “Not a majority, but I would guess a good number. I don’t think it means changing anything fundamentally. Our point of view is our point of view.” Even so, said Jen Flanz, another executive producer of the show, “we are trying to see all sides of it.”

Comedy Central has grappled with weaker TV ratings for Noah’s “Daily Show” since it launched, but executives believe the recent election has fueled new interest in a host who is gaining more confidence on screen. “It’s fair to compare Trevor to Jon, as long as it’s not comparing Trevor’s beginning with Jon’s end,” said Kent Alterman, president of Comedy Central, in an interview. “We brought Trevor in because of his talent and his brain, but not because of his experience, and we always expected to take some time before he really took control of the show.”

The network took pains to tie “Daily” closely to the election cycle, airing multiple live broadcasts around debates and conventions. Viewership for “Daily Show” bounced higher as the big day drew closer. In October, overall linear TV viewing among people between 18 and 49 rose 16%, while total viewers rose 15%. In terms of overall TV audience, “Daily” tends to fare better than TBS’ “Conan” among daily rivals, but not as well as its late-night broadcast competitors.

Comedy Central has placed emphasis on Noah’s traction among younger viewers who stream the program at times of their own choosing. More than one-third of overall consumption of the first year of Noah’s “Daily” came from digital viewing, compared with just 16% in the year-earlier period. Since Noah debuted, multiplatform streams are up 57% for Noah’s “Daily Show,” driven by triple-digit percentage increases across Facebook and YouTube.

The program has something that many of its direct rivals do not – a wide array of correspondents who hail from different backgrounds. On any night, a viewer might see Roy Wood Jr. quaffing Pepto-Bismol as election results come in; Ronny Chieng on the streets of New York City trying to cajole passers-by to take part in a poll; or Desi Lydic reporting from one chaotic scene or another. The assemblage gives “Daily Show” license to tackle a topic from any number of perspectives – a feat that its contemporaries,  nearly all led by white men (save Chelsea Handler’s program on Netflix and Samantha Bee’s weekly TBS series) cannot.

“It’s a really young, diverse, smart cast,” said Flanz. “It’s a really important voice right now.”

Producers say they have tried to find new cracks in the culture to mine.  Stewart often got attention by railing at the cable-news networks. He famously contributed to the shut-down of CNN’s venerable “Crossfire” by going on that program and telling the hosts their arguing did nothing to inform their viewers, and meted out similar scorn to CNBC and Fox News Channel. But Bodow said the show’s current viewership is focused less on those outlets.

“The media is not what it used to be, and cable networks are only one part of the total media environment. I think Trevor’s own sort of media diet is much more similar to our audience’s,” he said. Examinations of the media these days might include fake news being distributed on Facebook, not what Bill O’Reilly or Anderson Cooper said the night before.

Meanwhile, Noah has quietly been traversing America, doing live comedy shows across the nation, which has helped him form more trenchant observations of its populace. “He’s a guy who took Trump’s candidacy seriously early on,” said Alterman. “He didn’t treat it as a joke.”

Of course, that won’t stop the host from making jokes about the new president and his policies – and perhaps sounding an alarm when necessary. “This is a seismic shift,” said Bodow of the aftermath of the U.S. election, vowing that “Daily” will keep pace in weeks to come. “Suddenly, we are looking at a horizon that doesn’t really have an end date on it.”