I want to be sure that I did this right before I proceed as I'm unsure if my answers are 100% correct.

Graph the rational functions and include the equations of the asymptotes and dominant terms.

y=(-3)/(x-3)

So to find the horizontal asymptote I find the limit as x goes to infinity and negative infinity. As x goes to infinity the limit is 0 approaching from the left. As x goes to negative infinity the limit is 0 approaching ffrom the right. so the equation is y=0

To find the vertical asymptote I set the denominator equal to 0 and find the limit as x approaches the number that satisfies it. In this case 3. So the limit as x goes to 3 from the right is negative infinity. I plugged in 3.0001 for x. For x approaching from the left I plugged in 2.9999. Limit was infinity. so the equation is x=3

My problem is looking at these asymptotes they seem to contradict each other when I go to make the graph. Or...perhaps I'm just looking at them wrong.