Continuous vs. Discrete: Finding Domain and Range **I highly recommend that you take notes regarding the 2 types of data. Especially the difference between set notation and interval notation.** We will have to determine and write domain and range differently depending if the data is discrete or continuous (click each below 👇): For continuous data, you will need to use interval notation to describe domain and range. Here is the domain and range in interval notation for this example: D: 0≤x≤4 R: 0≤y≤12
Understanding the difference between continuous and discrete data is important because it affects how we describe the domain and range of a function or set of data.
Continuous data can take any value within a given interval and are often represented by measurements. For continuous data, any value between two given points is valid. Hence, when we denote domain and range for continuous data, we use interval notation. Interval notation is written with brackets or parentheses to indicate whether the endpoints are included or not.
- A closed interval `[a, b]` includes the endpoints, meaning `a` and `b` are part of the interval.
- An open interval `(a, b)` does not include the endpoints, meaning `a` and `b` are not part of the interval.
- A half-open interval `[a, b)` or `(a, b]` includes one endpoint but not the other.
For example, if you're given a continuous function where the input variable `x` can range from 0 to 4, including the endpoints, and the output variable `y` can range from 0 to 12, also including the endpoints, in interval notation you would write:
Domain of `x`, D: `[0, 4]` (This means `x` can be any number between 0 and 4, including 0 and 4.)
Range of `y`, R: `[0, 12]` (This means `y` can be any number between 0 and 12, including 0 and 12.)
Discrete data, on the other hand, can only take on specific, distinct values, often represented as points. For discrete data, we typically use set notation, listing out the elements of the domain or range when they are finite, or using inequalities to describe them if they are countably infinite.
Let's look at an example for discrete data. If we have a set of data where the domain is the set of natural numbers less than 5, and the range is the set of multiples of 3 less than or equal to 12, we can use set notation to describe the domain and range as follows:
Domain of `x`, D: `{0, 1, 2, 3, 4}` (x can only be one of these specified values.)
Range of `y`, R: `{0, 3, 6, 9, 12}` (y can only be one of these specified values.)
It's important to choose the correct notation based on whether the data is continuous or discrete to clearly communicate the nature of the data and allow for accurate interpretations by others.