Sorry, can't help with the first two. You provided insufficient information. You didn't provide the operation that is happening in the first problem, and you didn't give the original coordinates of p in either problem.
As for the other two problems, read on:
Discussion
Horizontal Asymptotes
There is never more than one horizontal asymptote.
Compare the degree of the numerator polynomial to the degree of the denominator
polynomial.
If the degree of the denominator is larger than the degree of the numerator,
then the horizontal asymptote is always . In other words, the
function is asymptotic to the x-axis.
If the degree of the denominator is smaller than the degree of the numerator,
then there is no horizontal asymptote. There is, however, a slant asymptote.
To determine the slant asymptote, use polynomial long division. The equation
of the slant asymptote is equal to the quotient excluding the remainder.
If the degree of the denominator equals the degree of the numerator, the
horizontal asymptote is at y = a where a is the quotient of the lead
coefficient on the numerator divided by the lead coefficient on the
denominator.
Vertical asymptotes
There is one vertical asymptote for every real zero of the denominator
polynomial.
Set the denominator polynomial equal to zero and solve for all real roots.
The vertical asymptotes are then , , ...,
Where through are all of the real roots of the
denominator polynomial.
Solution
I'm going to show a solution for your first problem, then you should be able
to solve the other one.
Horizontal: The degree of the numerator is 1. The degree of the denominator
is 1. The lead coefficient on the numerator is 2 and the lead coefficient on
the denominator is 1.
Therefore, the horizontal asymptote is
Vertical asymptote: Set the denominator equal to zero and solve.
Therefore the vertical asymptote is . Since the denominator
polynomial is of degree 1, we know that there is only one real zero of the
polynomial and therefore only one vertical asymptote.
Check Answer
The graphing system on this site doesn't handle functions with vertical
asymptotes very well, so ignore the sort of vertical line on the graph
above. Note that there is a vertical line at that the graph
does not intersect, and a horizontal line at that is approached
by the function as the absolute value of x gets very large.