Which of the following is a sign of hypoxia in a patient?

Cyanosis of the skin is a sign of hypoxia, which occurs when there is insufficient oxygen being delivered to the tissues. The bluish discoloration of the skin, especially evident in areas such as the lips, fingertips, and earlobes, indicates that hemoglobin is not sufficiently saturated with oxygen. This condition can arise from various causes, including respiratory issues, cardiovascular problems, or high altitudes, and serves as a visual cue for health care providers that the patient may be experiencing inadequate oxygenation.

In contrast, the other options present indications that do not align with signs of hypoxia. Increased energy levels would typically suggest adequate oxygenation; a decreased heart rate may occur in certain conditions but is not directly indicative of hypoxia; and a normal respiratory rate often suggests that the respiratory system is functioning properly and oxygen delivery is adequate.