In each of the following examples, a consumer purchases just two goods: x and y. Based on the information in each of the following parts, sketch a plausible set of indifference curves (that is, draw at least two curves on a set of labeled axes, and indicate the direction of higher utility) and state why this may occur. Also, write down a utility function u(x, y) consistent with your graph. not all will be monotone.

U(x,y)=(x^2)(y)

U(x,y) = x+1/(2y)