2. Consider the quadratic function f(x) = 4x* + 4x 15. a) Write an equation of the reciprocal of f(x); name this new function g(x). b) State the domain and range of both f(x) and g(x). c) Specify the x-intercept(s) and y-intercept(s) of both f(x) and d) Write the equations of any asymptote(s) on g(x); specify which. e) Discuss the end behaviour of f(x) and behaviour near the asymptotes for g(x). f) Find the interval(s) where f(x) and g(x) are positive and/or negative. g) Find the interval(s) where f(x) and g(x) are increasing and/or decreasing. h) ldentify any symmetry for both functions. i) Sketch accurate graphs of f(x) and g(x) on the same grid; show main key features including any max/min points. o o o - r e o wmo; -~ @ W 09 8 -7 6 5 4 3 -2 - =i b b L bbb R A 01 2 3 4 5 &6 7T &8 &5 10