On the most basic level of definition, humans are simply living organisms. To deny this would deny the most basic and fundamental aspect of being human. With being living organisms comes the good – namely our ability to think, feel, experience, etc. – but also the bad, such as some of our appetites. Regardless of what these may be, the fact that we are all living organisms at the most basic sense, before any names or positions are given, is chiefly important.
To begin, when we consider what a function for humans might be before labels like carpenter or father, we could look to the apparent functions of organisms in general. Should we look at a bear we might say it's function is to catch fish and eat them, or a dolphin's function is to swim. But this is still not the most basic form of their functions. A bear does not catch fish because it finds enjoyment in the act of fishing, nor does a dolphin swim merely for the enjoyment of swimming. In fact, it would seem that in the case of most living organisms before we attribute labels or names to their roles, the functions we could attribute to them (i.e. catching fish, eating, running, flying, etc.) are not done for the intrinsic values that they hold. There seems to be a single level deeper.
I would then argue that this level is the idea of survival. At the most basic level, living organisms are intrinsically willed to survive. In the case of the bear, she does not catch fish for the pleasure in it but for the food that it provides to her and her young. So too does the dolphin swim so it might escape hunters and hunt for itself. In most living organisms, it would seem that this, survival, is the most basic of functions, and as such it would seem that this would apply to humans as well.
Now, if we accept this idea, that survival is the most basic function of man and living organisms, we might be satisfied. However, should we study it deeper, I feel that some questions arise which need answering. For one, why do we wish to survive? In the end, it is simply an uphill battle that we will never win. No matter how well we survive, no matter how excellent our survival skills are, we will still eventually die. And secondly, what is the end of survival? We have labeled it as intrinsically good, so it should just be surviving, but then if we all die, how can this be the highest form of good for man if it is, in its entirety, unattainable? It should follow that our function should be one that can be completed, or else we could never label a good human or a bad one. Is a human who dies younger worse than one who dies old, regardless of the fact that they both no longer exist? This wouldn't follow as they both, no matter what, have met the same end. So, this leads us to two possible outcomes in my opinion, chiefly that a) our function is death or b) we have no function.
The idea that our function is death seems to have its merits, albeit morbid ones. Since all humans die, it is attainable, so already it has a leg up over survival. But then when we ask about the idea of excellence in death, just as we have with survival, we run into a wall once more. How do we describe or label an excellent death? Is it based on the grounds that it was painless and unexciting, or is a gruesome or brutal death more 'excellent'? Neither of these options seem to be viable, so perhaps just the act of dying is excellent in itself. However, if this is true our first stipulation goes to the wayside as no one can not die, so then there is no way to measure the function. With this, it would seem that neither survival nor death are reasonably our function.
Thus we arrive at the final conceivable option to me, that being the idea that there is no function. We as humans, and living organisms, have no actual attainable goal or purpose in life or death. Our existence is in-and-of-itself absurd and incredible, but otherwise holds no real value in the end – so it would seem. Especially if we look at things on the grand scale, how our actions impact ourselves, each other, the world, the universe, etc., we find that our feats – heroic or rational – seem to hold no meaning beyond our small-knit community of living organisms. Nothing we do seems to impact further than the atmosphere of this world, and even as we explore deeper into the infinite we have no power there. So it would seem that our function as humans, as living organisms, is non-existent. Granted, I have not explored the ideas of the divine, but I feel should we go down the road of religion we would eventually end up on this same path.