Find any pint of discontinuity for each rational function. Describe any vertica; pr horizontal asymptotes and any holes.

y=(x^3-1)/(x^2-1)

Question

Find any pint of discontinuity for each rational function. Describe any vertica; pr horizontal asymptotes and any holes.

y=(x^3-1)/(x^2-1)

anonymous · Answer

sorry but i dont know that answer i dont really know algebra 2

anonymous · Answer

Hey, bro =D
Discontinuity in rational functions comes from the fact that we can't divide by 0. Why can't we divide by 0? Well, think about an expression like:
$$\frac{3}{0} = a$$
We could multiply both sides by 0, and we would get
$$3 = 0*a$$
Can we come up with any answer "a" so that that will be true? No, because whatever we pick, a*0 will be 0.

So! Figure out what values of x make you divide by 0 in your functions. That's where you will have discontinuity.

anonymous · Answer

Thanks

anonymous · Answer

Once you know those points of discontinuity, the same points will usually have a vertical asymptote. The only exception to that is if I have a factor on top and bottom like this:
$$\frac{4x(x+3)(x-1)}{x-1}$$
in a case like this, x cannot be 1, because that would make me divide by 0, but since (x-1) is also in the top, you get a hole instead of a vertical asymptote.
Feel free to ask me any questions that come up =)