Finding the asymptotes of an odd function The question gave the graph shown below, giving one asymptote as $y=f(x)=\frac{1}{2}x - 3$. Graph: 
I was asked to complete the rest of the graph and draw on any missing asymptotes, and this is what I drew: 

For the other asymptote which I drew I wasn't sure what its equation was but I predict it's $y=\frac{1}{2}x + 3$. My question is how would I know for sure that that is the equation of the second asymptote without just guessing?

the given asymptote means
$$\lim_{x\to -\infty}(f (x)-(\frac {1}{2}x-3))=0$$
but $f $ is odd $ (f (-x)=-f (x)) $.
replacing $x $ by $-x $, we get
$$\lim_{x\to+\infty}(f (-x)-(\frac {-1}{2}x-3))=0$$
$$\implies$$
$$\lim_{+\infty}(f (x)-(\frac {1}{2}x+3))=0$$
thus the other asymptote is
$$y=\frac {1}{2}x+3$$
