Rasputin had influence over government decisions when he was close to the Czar's family. How does this support the claim that the government was corrupt?

Well Rasputin was mostly trusted by the Zar's family because he was always called upon on when there son was ill and when they wanted to know about what was going to happen to them later on. So the Zar family depened on Rasputin and believed what he said and also know that Rasputin told them false statements because he wanted to overthrow the Zar family so he could become the Zar.