Algebra 2 · Unit 1 · Topic 1.1
Function Domains and Multiple Representations
A function assigns one output to each allowed input.
Definition and explanation
A function assigns one output to each allowed input. Its domain must respect algebraic restrictions and any restrictions of its context; formulas, tables, and graphs describe the same relationship in different ways.
Worked example
For f(x) = √(x − 4)/(x − 7), the square root requires x ≥ 4 and the denominator requires x ≠ 7. Thus the real domain is [4, 7) ∪ (7, ∞). For instance, f(8) = 2.
Common mistake
Checking only the denominator can miss a square-root restriction.
Key takeaway
A function assigns one output to each allowed input.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.