Final answer:
Function f, which assigns historical average high and low temperatures to each day of the year, qualifies as a function because each day is paired with a unique set of temperature values. In a graphical representation, this would be depicted on a time series graph reflecting the temperatures' chronological sequence.
Step-by-step explanation:
The description of f indicates that it is a function because it relates each day of the year to the historical average high and low temperatures in New York City for that date. A function in mathematics describes a particular kind of relationship where each input (in this case, each day of the year) is related to exactly one output (the average high and low temperatures). Therefore, unless there are multiple average temperatures listed for a single day, the description suggests that f is indeed a function because each day has a unique set of temperature readings associated with it.
When analyzing data over time, a helpful visual tool is a time series graph, which would show how the temperatures change day by day, reflecting the chronological order. In climate studies, historical data is crucial since we cannot directly measure past climates; instead, historical averages give us insight into climatic patterns. This conceptual understanding is important when considering temperature as a dynamic variable and constructing statistical models or predictions, like estimating future temperatures or the effects of a cold front.