How to know when given secure PRNG, modified PRNG is secure or insecure?

I'm having trouble to distinguish modified pseudo-random generators when given G: {0, 1}^s --> {0, 1}^n is a secure PRNG. I want to know whether some G's are secure PRNG or not. And I also want to know the reason why it can be distinguished from a real random generator.

These are G'(k)s...

G'(k) = G(k)||G(k+1)

G'(k) = G(k)||G(2*k)

G'(k) = G(k)||k

Thank you for your answering!