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.
I guess I mean when I go to graph the equation with the asymptotes, it seems like I did something wrong because i would be graphing the equation as x goes to 3 from the right and the limit is negative infinity. So im a little confused as it seems thats impossible as it would seem the limit would have to be positive infinity for that certain side limit.
Yah I graphed it on my calculator gave me an idea of how to graph it though I was just confused that on the graph it seems it comes from negative infinity to 3 from the left and not the right as specified in the asymptotes if that makes sense. perhaps im thinking too much