Final answer:
The relationship between breathing frequency and body size is an A) inverse relationship. As body size increases, breathing frequency decreases due to differing metabolic rates per unit body mass. This is distinct from positive and negative correlations where variables increase together or inversely affect each other, respectively.
Step-by-step explanation:
The relationship between breathing frequency and body size is an inverse relationship. This means that smaller animals tend to have higher breathing frequencies, whereas larger animals breathe less frequently. This can be explained through the metabolic rates of animals, where smaller animals generally have higher metabolic rates per unit body mass and thus require more oxygen, leading to a higher breathing rate.
An example that illustrates an inverse relationship can be seen in Australian mammals, where population density decreases with increasing body size. Similarly, the depth of an air column and the frequency of pitch generated show an inverse relation.
In the context of correlations, a positive correlation implies that as one variable increases, the other variable also increases. For instance, height and weight typically have a positive correlation: as one's height increases, their weight tends to increase as well. On the other hand, a negative correlation suggests that an increase in one variable leads to a decrease in the opposite variable, such as between tiredness and hours of sleep.