A $5 ticket is sold to at most 60 students: R(n) = 5n.
Show answer
Domain: {0, 1, …, 60}; range: {0, 5, …, 300}.
Free printable worksheet
Domain and Range Word Problems Worksheet
Twelve real-world problems identifying practical domains and ranges from discrete and continuous situations.
Algebra 1Grades 8-114 pagesAnswer key included
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What this worksheet includes
- Twelve real-world problems identifying practical domains and ranges from discrete and continuous situations.
- 4-page printable PDF with a complete answer key
- Designed for Grades 8-11 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this domain and range word problems worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
If students need more practice with notation and function families first, begin with the foundational domain and range worksheet.
Who this practice is for
This resource is designed for grades 8-11 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach domain and range word problems
A practical domain contains only input values that make sense in a situation. A ticket count must be a whole number, while time, distance, width, and temperature can usually vary continuously across an interval.
The practical range is the set of outputs produced by that restricted domain. Start with the mathematical rule, apply the contextual restrictions, and then decide whether set notation or interval notation communicates the result clearly.
Learning objectives
- Interpret domain and range in context
- Distinguish discrete from continuous quantities
- Write practical restrictions in set and interval notation
Skills to review first
- Function notation
- Evaluating expressions
- Reading inequalities and interval notation
Worked example
Follow the reasoning step by step
A museum charges $8 per ticket and can admit at most 150 visitors. If R(v) = 8v, find the practical domain and range.
- The input v counts visitors, so it must be a whole number.
- The museum can admit from 0 through 150 visitors.
- Evaluate the endpoint outputs: R(0) = 0 and R(150) = 1,200.
- Revenue increases in steps of $8 because partial visitors are not possible.
Solution: Domain: {0, 1, …, 150}. Range: {0, 8, …, 1,200}.
Try before downloading
Domain and range word problem examples with answers
Work each problem, then open the answer to check your result.
A runner travels from 0 through 10 miles: d(t) = 2t.
Show answer
Domain: [0, 5]; range: [0, 10].
h(t) = −16(t − 2)² + 64 for 0 ≤ t ≤ 4
Show answer
Domain: [0, 4]; range: [0, 64].
Error check
Common mistakes to watch for
- Using all real numbers when the situation limits the inputs
- Writing an interval for a count that must use whole numbers
- Finding the endpoint outputs without checking for an interior maximum or minimum