Problem 118 - Precalculus Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. My body temperature is a function of the time of day.

Step-by-Step Solution

Answer

The statement 'My body temperature is a function of the time of day' does not make complete sense because body temperature can be influenced by various factors apart from the time of day, and hence there isn't a unique body temperature for every specific time of day.

Step 1: Understand the concept of a Function

A function in mathematics is a relation between two sets that associates each element of the first set to exactly one element of the second set. In simpler words, a function is a relation where each input has a unique output.

Step 2: Analyze the statement

The statement says 'my body temperature is a function of the time of day'. In terms of a function, 'the time of day' is the input and 'body temperature' is the output. This statement implies that each specific time of the day results in a unique body temperature.

Step 3: Reasoning and conclusion

The body's temperature does fluctuate mildly throughout the day - it is usually slightly cooler in the morning and slightly warmer in the afternoon. However, the statement assumes that for every specific time, there will be a predictable, unique body temperature, which is not accurate. Several factors can influence body temperature, such as physical activity, clothing, weather, illness, etc., regardless of the time of day. Hence, the statement does not make complete sense.