In mathematics, range, also known as co-domain, is a fundamental concept closely associated with functions, mappings, and sets. It refers to the set of all possible output values that a function or mapping can produce for a given set of input values or the subset of a set represented as a set.
What is Range in Math?
Range is a mathematical term used to describe the difference between the highest and lowest values in a set of data. It’s a measure of how spread out your data is. A smaller range indicates that your data is more clustered together, while a larger range indicates that your data is more spread out. Here’s a breakdown of the range formula:
Steps to Calculate Range:
- Find the highest and lowest values in the data set.
- Subtract the lowest value from the highest value.
- The result is the range.
Example:
Suppose you have the following data set:
{1, 3, 5, 7, 9}
The highest value in this set is 9, and the lowest value is 1. So, the range is:
Range = Highest value - Lowest value
Range = 9 - 1
Range = 8
Additional Notes:
- Range is a simple and straightforward measure of variability.
- It’s not affected by outliers, which are extreme values that are much larger or smaller than the rest of the data.
- Range is often used in conjunction with other measures of variability, such as standard deviation and variance.
Table Summarizing Key Points:
| Term | Definition |
|---|---|
| Range | Difference between the highest and lowest values in a data set |
| Highest value | Largest number in a data set |
| Lowest value | Smallest number in a data set |
Question 1:
What is the definition of ‘range’ in mathematics?
Answer:
Range is a mathematical term that refers to the set of all possible outputs of a function. It is also known as the codomain or image of the function. The range is typically denoted by the symbol R.
Question 2:
How is the range of a function determined?
Answer:
The range of a function can be determined by finding the set of all possible values that the function can output. This can be done by evaluating the function at all possible input values. Alternatively, the range can be determined by using the function’s inverse function.
Question 3:
What is the relationship between the range and domain of a function?
Answer:
The range and domain of a function are two related sets. The domain is the set of all possible input values of the function, while the range is the set of all possible output values. The range of a function is always a subset of the codomain of the function.
Thanks for sticking with me through this intro to range. I hope you now have a clear understanding of what range is and how to find it. If you’re still a bit fuzzy on the details, don’t worry – just come back and give this article another read later. I’ll be here, waiting to help you get your math on!