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The autonomic nervous system is divided into the sympathetic nervous system and the parasympathetic nervous system. The effector organs are surrounded by parasympathetic ganglia, which have long preganglionic fibers and short post-ganglionic fibers.

The increase in the heart rate is managed by the sympathetic branch of the autonomic nervous system. The sympathetic branch releases hormones like epinephrine and norepinephrine to manage the heart rate.

Thus, an increase in heart rate is not a function of the parasympathetic branch.

Therefore, the given option is incorrect.

The function of the parasympathetic branch of the autonomic nervous system includes the increase in the body's digestion. The parasympathetic branch conserves energy that is used for activities like digestion and urination.

Thus, enhancing digestion is the function of the parasympathetic branch.

Therefore, the given option is correct.

The release of epinephrine is the function of the sympathetic branch of the autonomic nervous system. The adrenal gland, along with the post-ganglionic fibers, releases the epinephrine and norepinephrine hormone.

Thus, triggering the release of epinephrine is not a function of the parasympathetic branch.

Therefore, the given option is incorrect.

The conversion of glycogen to glucose is done by the hormone glucagon released by both the parasympathetic and sympathetic branches. The parasympathetic branch stimulates, and the sympathetic addition inhibits its secretion into insulin.

Thus, the conversion of glycogen to glucose is the function of both the sympathetic and parasympathetic branches.

Therefore, the given option is incorrect.