Final answer:
The data does represent a function since each age corresponds to one height. The domain is the set of ages, and the range is the constant height of 160 cm. In a typical growth pattern, heights when plotted against age would show variability and often follow a normal distribution.
Step-by-step explanation:
The student is asking whether the relationship between height and age in the provided data represents a function. In mathematics, a relation is a function if every input corresponds to exactly one output. In the context of this question, the input is the age, and the output is the height. Looking at the data, the height remains constant at 160 cm regardless of the age. This does mean it is a function, as each age (input) does uniquely correspond to one height (output).
If we define this as a function, the domain of the function would be the set of ages given: {20, 25, 30, 35, 40, 45}. The range would be the set of heights, which in this case is simply {160} because the height does not change with age in this dataset.
To provide a real-world example of functions in height and age, consider a typical growth of a child. Data might show that at different ages, a child has different heights. This type of relationship often follows a normal distribution, as heights across a population are distributed in this way. Considering a scenario where the mean height is provided along with standard deviation, one can calculate z-scores to assess how an individual's height compares to the mean population height.