Everyday usage and use in mathematics
The word range usually refers to the extent or scope of something. The Oxford English Dictionary defines range[1] as 'The area of variation between the upper and lower limits on a particular scale', essentially meaning, the minimum and maximum value of something, and everything between. For instance, we might say that a singer has a wide vocal range, meaning they can sing notes from low to high. Similarly, the range of a car refers to the maximum distance it can travel on a full tank of fuel. In mathematics, the range refers to the set of all possible output values a function can produce, which aligns with the idea of covering the full extent from minimum to maximum.
Importance in mathematics
In mathematics, the range of a function is the set of all possible output values it can produce. Just as a singer's vocal range defines the limits of the notes they can hit, and the range of a car tells us how far it can travel, the range of a function defines the extent of its possible outputs. This mathematical concept is crucial for understanding the behavior of functions and their applications.
Comparison
The comparison between everyday usage and mathematical usage of range reveals a shared underlying idea: the full extent of potential outcomes. Whether describing the notes a singer can hit, the distance a car can travel, or the values a function can generate, range always conveys the idea of limits and extents.
Exercises
- Everyday Context: List three more examples of how range is used in everyday language.
Example: The range of temperatures in a desert. - Mathematical Context: Given the function \( f(x) = x^2 \), determine its range.
- Comparison: Explain how the concept of range is similar in both everyday and mathematical contexts using your own words.
References
[1] Oxford English Dictionary, s.v. “range, n.”, https://www.oed.com/dictionary/range_n