1. Consider the function f : E } 5 dened by ny] = (3353?3 + yg} for all {my} E E. [a] Prove that f is a transformation and nd a formula for f_1(3:, y}. [b] Show that f is not. an isomet-ry. {c} Find all xed points of f. [d] Describe the images of straight lines under the transformation f. Find the equations of the lines which are mapped either to a ne or to a parabola. {e} Find the equations of f} and f[m}, where f is the line with equation 1; = 5 and m is the line with equation I = . 2. [a] Find the coordinates Dfpif[Q} when P = [1,1} and Q = [3,3}1 as well as when P = {1,1} and Q = {11}. [b] Identify precisely the following isometries. [Give complete information, not just a classication into type.) {i} cream, when E has equation 3; = l + :r and 131 has equation 3; = 4 1'. [ii] cream, when E has equation 3; = a.' 2 and 111 has equation y = via: +1]. 3. [a] Given a vector u and a point P, what kind of isometrj.r can be the composite qpru'? [b] Identify 1::-ret:::isel},r the isometr},r fm'm when E has equation 32;; = U, m has equation a: + y + 5 = and n has equation 23 2;; + 1 = I). [Give complete information1 not just a classication into type.)