Final answer:
The 1st-order neuron in the hypothalamospinal tract transmits signals from the hypothalamus to the lateral horn of the spinal cord at T1, and is involved in regulating sympathetic output.
Step-by-step explanation:
The function of the 1st-order neuron in the hypothalamospinal tract is to transmit signals from the hypothalamus to the lateral horn of the spinal cord at the level of T1. This tract plays a role in the autonomic nervous system, specifically in regulating the sympathetic output from the spinal cord. The 1st-order neuron carries signals related to sympathetic responses, such as the control of sweat glands in the skin and blood vessels supplying skeletal muscle.