Yes, it is - centred around the mid-grey, and you define what range you want to cover on the x axis (black and white relative exposure), how steep the mid-section should be (contrast), how wide the constant-steepness section should be (latitude), and where it should be located (shadows/highlights balance).
Much of the discussion under New Sigmoid Scene to Display mapping is how such curves should/could be implemented. Aurélien gives his reasons in that topic, others suggest different approaches.