Discrete function
Identify discrete functions in Grade 10 algebra as functions with isolated, countable domain values, graph them as separate points rather than continuous lines, and model real-world counting scenar...
Key Concepts
A discrete function is a collection of separate, unconnected points. Instead of a smooth line or curve, its graph looks like a series of dots. This type of function is used when the input values are distinct and separate, such as counting objects, where you can't have fractional values. The domain and range consist of individual numbers.
The function representing the number of cars sold each day: $f = \{(1, 10), (2, 4), (3, 18), (4, 7)\}$. A graph showing the number of students in each grade at a school would be discrete points. The set of points $g = \{(1, 5), (2, 10), (3, 15)\}$ is a discrete function.
Picture crossing a river by hopping on stepping stones. You can only be on one stone at a time, not in the water between them. A discrete function is just like that—a set of separate points with nothing connecting them.
Common Questions
What is a discrete function and how does it differ from a continuous function?
A discrete function has a domain of isolated, countable values (like whole numbers). Its graph is a set of separate points, not a connected curve. Continuous functions have no gaps.
Give an example of a discrete function in a real-world context.
The number of students in a class as a function of year. You can have 25 or 26 students but not 25.7. The domain consists of whole number values only.
How do you graph a discrete function?
Plot individual points for each valid input-output pair. Do not connect the points with a line or curve, as the values between the plotted points are not in the domain.