Let f(x) = a(x −p )^2 + q be a quadratic function, where a, p,q are constants and a ≠ 0. f(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define f(x) be the function after performing all the transformations. a. Find the conditions on the constants a, q and k so that g(x) does not have a vertical asymptote.

b. Find the x value(s) so that there is/are invariant point(s) linking f(x) and 1/f(x).