What you will be able to do
- Work each problem without looking at the answer.
- Write the algebraic step that justifies each change.
- Check the result in the original relationship.
- Use the error notes to decide what to practise next.
How to use this worksheet
State domain and range using the representation requested. In context problems, include realistic restrictions and units.
- Read domain and range from ordered pairs
- Evaluate function notation
- Decide whether a relation is a function
- Apply contextual restrictions
For a clean student copy, print this page and cover the worked solutions or select the problem pages in your browser’s print preview.
Practice problems
Problem 1
For {(−2, 5), (0, 1), (3, 5), (7, −1)}, state the domain and range.
Problem 2
If f(x) = 3x − 4, find f(6).
Problem 3
Is {(1, 4), (2, 6), (1, 7)} a function?
Problem 4
A ride costs C(m) = 2.5m + 4 for 0 ≤ m ≤ 20. State a reasonable domain and range.
Problem 5
For g(x) = x², if the domain is {−3, −1, 0, 2}, find the range.
Answer key with worked solutions
Problem 1
For {(−2, 5), (0, 1), (3, 5), (7, −1)}, state the domain and range.
- 1.Domain is the set of first coordinates.
- 2.Range is the set of distinct second coordinates.
Answer: Domain {−2, 0, 3, 7}; range {−1, 1, 5}
Check: Repeated output 5 is listed once.
Problem 2
If f(x) = 3x − 4, find f(6).
- 1.Substitute 6 for x: f(6) = 18 − 4.
Answer: 14
Check: 3(6) − 4 = 14.
Problem 3
Is {(1, 4), (2, 6), (1, 7)} a function?
- 1.Input 1 is paired with both 4 and 7.
Answer: No
Check: A function assigns exactly one output to each input.
Problem 4
A ride costs C(m) = 2.5m + 4 for 0 ≤ m ≤ 20. State a reasonable domain and range.
- 1.Distance m is continuous from 0 to 20.
- 2.Minimum cost is C(0) = 4; maximum is C(20) = 54.
Answer: Domain [0, 20]; range [4, 54]
Check: Units are miles and dollars.
Problem 5
For g(x) = x², if the domain is {−3, −1, 0, 2}, find the range.
- 1.Square each input: 9, 1, 0, 4.
- 2.List distinct outputs in order.
Answer: Range {0, 1, 4, 9}
Check: Every listed output comes from a domain value.
Use mistakes to choose the next step
Graph linear equationsLearn exponential functions
| If this happened | Likely issue | Next practice move |
|---|---|---|
| First and second coordinates reversed | Domain/range order confusion | Say input first, output second |
| Repeated outputs treated as not a function | Function definition confusion | Only repeated inputs with different outputs break a function |
| Context domain includes impossible values | Missing restrictions | Ask what inputs the situation permits |
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Useful answers
Frequently asked questions
Can two inputs have the same output in a function?
Yes. A function fails only when one input has more than one output.
Does every equation have all real numbers as its domain?
No. Algebraic restrictions and the real context can limit allowable inputs.
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Sources, scope and accuracy
The worked examples and practice questions on this page are original Cambridge Veritas learning materials, not released STAAR items. Curriculum and testing details can change; use the linked Texas Education Agency pages for current official information. Cambridge Veritas is not affiliated with or endorsed by TEA.