Moment Generating Function of Standard Normal random variable

For standard normal form variable Z~N(0,1).
What is the Moment Generating Moment of M_z(t) of Z.

Defining X=u+oZ for real numbers u,r with r>0. what is the distribution of X?

Use the Moment Generating Function M_z(t) to find the moment generating function M(t) of X.

Can anyone help with any of these question?

Hey wrexlive1.

For the Normal MGF, you have to use a trick to complete the square. First try showing your work with the e^g(x) term (for some function g(x)) after you collect all the terms so we can go through it from there.