Transformation of graphs of the functions.

Question

How to graph functions like $y=x+\sin x$ or functions having addition or subtraction of different variables?

Answer 1

If you just want a rough sketch, consider the derivative: $y'=1+\cos x$. Unlike the derivative of sine wave (which alternates between $\pm $), this one is never negative, but it periodically drops to zero. This means the shape resembles a smooth staircase: quickly up, then level out, repeat.