Pleas show work

1. A box is to be constructed from a sheet of cardboard that is 20 cm by 60 cm, by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have? 2. Find the amplitude and period of y = -3cos(2x + 3). Use your calculator to graph the function and state its symmetry. Find the first positive x-intercept using your calculator's zero function. 3. Find two functions f(x) and g(x) such that fig(x)] = x but g[f(x)] does not equal x. 4. State the vertical, horizontal asymptotes and zeros of the rational function, f(x) = * + 3x + 2 x2 + 5x +4 Why is there no zero at x = -1? 5. Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots