Question

Anyone know how to calculate vertical asymptotes and holes?

Describe the vertical asymptote(s) and hole(s) for the graph of y=x-4/x^2+3x+2

Answer 1

@LifeEngineer

Answer 2

you can find holes by factoring your denominator and seeing if any terms cancel out. for example, x^2/x could be simplified to x (by dividing out the denominator), however in order to keep true to the original function, you have to include that x cannot equal 0 (because then your original function would have a divide by 0) so you have a hole at 0.
It would look something like this:

long story short, if you can cancel something in the denominator, theres likely a hole there.

as for asymptotes, you have to look at where else the denominator can be 0. if the denominator is 0 and its not at a hole in the graph, it is likely an asymptote. an example of this would be x=1/x
when x = 0, you get a divide by 0 and that results in asymptotes as x approaches 0

note how the graph approaches -infinity and infinity. it will never actually reach these because x cant actually be 0, thus, its an asymptote.

essentially try factoring your denominator and see where that takes you