An example of how to use the first and second derivatives:
Remember that f'(x) tells you what the slope does and f''(x) tells you the curvature. So start with iv) which tells us we have the horizontal asymptote y = 0 for large negative x. Then we know from viii) that the function is decreasing for x < -1. Since we also know from ix) that the function has a negative concavity for x < -1 as well. All this means that the function curves (ie. is not a line) downward from -infinity to x = -1. Since x = -1 is not a vertical asymptote, it curves down to some real value f(-1).
To give you an example of what the function might look like for (-infinity, -1] consider the function y = 1/x over the same domain.