continous piece wise function

Create a continuous function f(x) on the interval [-4, 4] by drawing its graph which meets these conditions; f (0) = 2,

f '(2) = 0, f '(-2) {is undefined, f "(0) = 0, f "(-1) is undefined. There is a point of inflection when x = 1 and a minimum at x = -2/3. The limit of f(x) as x approaches 4 is -2.

Ok. It seems pretty easy to do a continous piece wise function. I could have a two linear function from some point between greater than 1 to 4 and -2 to -1, then create a function that is a constant from 4 to infinity and from -2 to negative infinity. I could then create a sin function from -1 to some point greater than 1 This would creat sharp corners at -2, -1 which means the function would be continuous but not differentiable at those points. I could manipulate the period to have the sin function with a derivative of zero at x = 0, f'(0) & f"(0) both equal zero. I could manipulate the a & b of a sine function to have the inflection at 1 and minimum at -2/3 and a limit of -2 if I set y = -2 at x => 4. My question Is there a way to do this numerically without creating a piecewise function? If so, how?