Kim Kardashian Brings Lunch to Bruce Jenner Following His Gender Transition Reveal

The reality star was seen at his Malibu, California, home on Saturday

Photo: Splash News Online

Update: In June 2015, Caitlyn Jenner came out as a transgender woman. This content was written in April 2015, before Jenner publicly announced her full transition.

As Bruce Jenner revealed in his bombshell interview with Diane Sawyer, Kim Kardashian West has been the most supportive about his gender transition.

No surprise, then, that the day following his 20/20 interview – which the Kardashian-Jenner family watched as a unit – Kardashian West, 34, was photographed at her stepfather's Malibu, California, compound.

A source close to the family tells PEOPLE that "she went just to hang out and see how he's doing and brought him lunch."

It's been a big week, not just for Jenner but also his extended family.

"We really all support him," Kardashian West told Today host Matt Lauer in a promo for an interview set to air Monday. "Is it a hard adjustment? Yes."

Indeed, sister Khloé had the toughest time adjusting to her stepfather being born with "the soul of a female," as he phrased it in his interview.

Though Jenner, 65, stated multiple times that his main concern was his family, he decided that he couldn't "live a lie" anymore. " 'She' is not a lie," he said. "I can't do it anymore."

Ultimately, the athlete "just really wants to help people," a source told PEOPLE. "He is on a mission and has a lot to offer. … He wants to help make a difference for people struggling with empowerment.

"And it's not just about those who are transgender," the source continued, "but those who are bullied or face discrimination, whether it's racial, sexual, religious, any 'differences.' He feels very strongly about this."

Added another source close to Jenner: "[He] wants this to be taken seriously so that his situation can have the most positive impact on society's perception of the transgender community."

Bruce Jenner’s Journey to Transition