Given the graphs of $y=f(x)$ and $y=g(x)$, sketch the graph of $y=k(x)$

Question

I think I have solved this problem correctly, but I am a little unsure of whether or not the asymptotes I found are correct. My apologies for the picture, I realize it is a little small for clear reading.

Answer 1

The asymptotes you found are correct, but I'd write down more formally how you found the horizontal asymptotes, something like: "$\lim_{x\to\pm\infty}\frac{\frac12x+4}{-\frac14x-1}=\ldots=-2$, and therefore the horizontal asymptote is $y=-2$".