Continuous vs. Discrete Domains
Grade 9 students in California Reveal Math Algebra 1 learn to distinguish between continuous and discrete domains in the context of real-world functions. A continuous domain includes all real values in an interval — like time measured in seconds — so the graph is an unbroken line. A discrete domain includes only specific separate values — like whole numbers of students or tickets — so the graph shows isolated points. For example, the height of a ball over time is continuous (1≤t≤5), while the number of students in a classroom is discrete ({20, 21, 22, 23}).
Key Concepts
A continuous domain includes all real number values within an interval, meaning every point between two values is included. A discrete domain includes only specific, separate values — often integers or a limited set of numbers.
Continuous domain example: all real numbers from $1$ to $10$, written as $1 \leq x \leq 10$ Discrete domain example: only the whole number values $\{1, 2, 3, 4, 5\}$.
Common Questions
What is a continuous domain?
A continuous domain includes all real number values within an interval. Every point between two values is included, and the graph is drawn as an unbroken line or curve.
What is a discrete domain?
A discrete domain includes only specific, separate values — typically integers or a limited set of numbers. The graph shows isolated, unconnected points rather than a continuous line.
How do you decide if a real-world function has a continuous or discrete domain?
Consider whether the input can take on any value in a range (continuous) or only specific separate values (discrete). Time, distance, and temperature are usually continuous; counts of people or objects are discrete.
Is the height of a ball over time continuous or discrete?
Continuous. Time can take on any real value in the interval 0≤t≤5 seconds, so the graph is an unbroken line.
Is the number of students in a classroom continuous or discrete?
Discrete. You can only have whole numbers like 20, 21, 22, or 23 students — not 21.5 students. The graph consists of individual isolated points.
Which unit and grade level covers this skill?
This skill is from Unit 2: Relations and Functions in California Reveal Math Algebra 1, Grade 9.