Canada's Wonderland is accepting proposals for a new roller-coaster idea! In this roller-coaster you must have at least four extreme and three inflection points. THE FUNCTIONS YOU CAN USE ARE: A polynomial function of the form y = a(x -r)(x - s)(x - t)(x - v) A sinusoidal function of the form y = asin[k(x - c)] + dory = acos[k(x - c)] + d (where the x-values are measured in radians) An exponential function of the form y = a(b)*(x-c) + d A logarithmic function of the form y = alog [k(x - c)] + d > A rational function of the form y = I (x) g(x) . OTHER PARAMETERS: You must use at least four out of the six types of functions listed above: o Polynomial function o Either a sinusoid or co-sinusoid o Either and exponential or logarithmic function o A rational function. You can use one type of function more than once. For example, you may use a polynomial function at two or more parts of the rollercoaster. The domain for your roller coaster should be {t E R|0 S t s 180)} (Where t is the time in seconds) > The range for your roller coaster should be {h E R|0 S h S 300)} (Where h is the height in feet - the current tallest roller coaster is 460 feet!) * All functions must connect smoothly