Question

what would the asymptotes of this function look like?
y=5/x-3+2

Answer 1

Do you still need help?

Answer 2

assuming that you mean 5/(x-3) +2.
Look at the equation, x can not be equal to 3 because it would make the denominator zero, meaning divide by zero and that it would not exist. Therefore there is an asymptote at x=3.

To find the horizontal asymptote you have to take the \[\lim_{x \rightarrow \infty} \frac{ 5 }{ (x-3) } +2 \]
Taking that limit the denominator will go to infinity meaning that the fraction goes to zero, but you still have the +2. So there is a horizontal asymptote at y=2.
You also have to take the limit going to -infinity to confirm, but that will also go to y=2.

Answer: Horizontal Asymptote at y=2, Vertical Asymptote at x=3.