A vertical asymptote is an x value at which y approaches infinite. One example includes when the denominator of the function approaches zero at a certain point. For example, (x^2 + 3) / (x + 1) has a vertical asymptote at x=-1, since the denominator approaches zero as x approaches this point.
For an oblique asymptote, y generally takes the form of a linear function as x approaches infinite. This is the case when the highest term in numerator is one degree higher than the highest degree term in the denominator.
Examples include (5x^2 + 2) over 2x, where the oblique asymptote is (5/2)x, and even the linear function 2x+3 has an oblique asymptote of 2x
here's what happens:
1) the graph of f = x^2 is shifted 2 units to the right.
2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.
3) this final result is transformed up by 5 units.