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1. Given f(x) = x4 - 3x3 - 3x2 + 11x - 6 a) List all possible rational zeros of the given function (3pts) b) Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros. State clearly how you computed the number of the changes of the sings and what you use to determine the possible number of negative zeros. (4pts) ) Find one rational zero and use long division or synthetic division to reduce the degree of the polynomial and find all other real roots. Show all work. (5pts) d) State x-intercepts and find y-intercept. (2pts) e) Find end behavior. Explain how you do it. (3pts) Find additional points on each subinterval. (2pts) g) Graph the given function. Mark clearly all important points on axis. (4pts) 2. Given f(x) - 2_10x +24 a) Find the domain of the given function (2pts) b) Find vertical asymptotes and explain the behavior of the functions when x app asymptotes (5pts) c) Find horizontal asymptotes. Explain the end behavior. (4pts) d) Find x- and y-intercepts. (3pts) e) Use the information above to sketch the graph of the given function. Show all asymptotes, x- and y-intercepts and any additional points you use for graphing. (4pts) 9 . 3. The height y (in feet) of a punted football is approximated by y = - + - where x 2025 Ex+ is the horizontal distance (in feet) from where the football is punted. a) How high is the football when it is punted? (Hint: Find y when x = 0) (2pts) b) What is the maximum height of the football? (4pts) c) How far from the punter does the football strike the ground? (3pts)