Is it true that cosmic microwave background radiation is the image of the Big Bang?

Not exactly. The physics at very high energy like the Big Bang conditions is still unknown. This is why we build big accelerator to try to reproduce and observe those conditions. But we know that few instants after the Big Bang the very high energetic radiation was created and started to expand. Once the energy density was lowered enough (20,000 years after the BB), the radiation started to produce particles and then, many billions of years later, us.

Not all the radiation converted in particles, a fraction remained radiation and it is still traveling in the universe. This is the microwave background radiation. So it is a remain of how the universe was in the first 20,000 years of its history.

Yes, the radiation known as cosmic microwave background radiation is thought to represent an early universe snapshot and to be the leftover heat from the Big Bang.