State the conditions on k such that the graph of has:

a) two vertical asympototes

b) only one vertical asymptote

c) no vertical asymptotes.

Answers:

a)

b)

c)

However if the equation above were to have two vertical asymptotes wouldn't the factorised denominator of the equation above be:

or or or

So wouldn't or ? If not, why not?

And if it were to have only one vertical asymptote, the equation with the factorised denominator would be or

Hence makes sense.

If the equation were to have no vertical asymptote, wouldn't x simply equal x=0? If x did equal zero, how would you find the range of values for k with no vertical asymptote?

Any help regarding questions a and c above and how to get the answer would be appreciated!