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Here, we draw indifference curves of several utility functions. Well, our motivation is to draw them, picking up points and convincing ourselves, that yes, this is indeed the shape of an indifference curve.

We know it well, that, along an indifference curve, utility is constant, so, we choose any arbitrary value of a utility and then pick points of x and y, which, according to a given utility function, results in the same utility (as our choosen arbitrary utility)

Let us do this exercise for our basic preferences, say, perfect complements, perfect substitutes, max utility function and cobb douglas

Draw an indifference curve for perfect substitutes

Draw an indifference curve for perfect complements, where u=min{x,y}

Draw an indifference curve for max function, u=max{x,y}

Draw an indifference curve for cobb douglas utility function, u=xy