/sci/ - Science & Math

I'm taking complex analysis and I missed two classes this week. We don't have a textbook and my teacher's posted notes aren't very helpful. So, I have a question about this problem. I understand how complex functions work as mapping some value from one complex plane to another complex plane(the x,y to u,v business). It's easy enough to figure that out. But I'm a bit confused when we start thinking about "strips".
Here is what I figure: the first strip is just saying that the magnitude of the real part of z cannot exceed one, so its all points between -1 and 1 on the real axis, and all on the imaginary. Similarly, the second strip is just a horizontal strip between 1 and 2 on the imaginary axis where x can be any value. But how do we show or describe the mappings?
So, for the first complex function (w = 2z +i), when we sub in (x+iy) for z, we find the real part becomes scaled by two in the image. So then, could we say that the image is defined by the magnitude of the real part being less than 2? For the second strip given, by similar logic, could we say that image is defined by the imaginary part being between 3 and 6(because v = 2y+1)? That's the only thing that makes sense to me, let me know if am on to something because the next questions are way harder.