Free Printable WorksheetMathAlgebra IIMath CurriculumF-IF.1

ALG2.70 Identifying Whether a Relation Is a Function Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.70 Identifying Whether a Relation Is a Function. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.70 Identifying Whether a Relation Is a Function - Select the correct use of mapping diagrams, tables, graphs, and the vertical line test to decide whether a relation is a function. Associated source-listed standards: CCSS F-IF.1; CA CCSSM F-IF.1; MA 2017 F-IF.1; NY NGLS F-IF.1; TX TEKS Algebra II: §111.40.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.70 Identifying Whether a Relation Is a Function skill assessments:

Problem 1Difficulty: Mastery

Which statement best summarizes when a relation is a function?

AEvery output must be used exactly once.

BEach output must correspond to exactly one input.

CA graph must be symmetric about the y-axis.

DEach input must correspond to exactly one output.

Solution & Explanation:The defining rule for a function is about inputs: every input has one and only one output. Outputs may repeat.

Problem 2Difficulty: Mastery

Let P be y = x², Q be x = y², R be {(1,3), (2,3), (4,5)}, and S be a mapping with arrows a -> 1, b -> 2 and b -> 4. Which pair of relations are both functions of x or of their listed inputs?

AP and Q

BQ and S

CP and R

DR and S

Solution & Explanation:P is a function, and R is also a function because each listed input has one output. Q is not a function of x, and S is not a function because b has two outputs.

Problem 3Difficulty: Mastery

Three students make these claims: Statement 1: A relation can be a function even if two outputs are the same. Statement 2: If one input has two outputs, the relation is not a function. Statement 3: Every inverse of a function is also a function. Which choice is correct?

AStatements 1 and 3 only are correct.

BStatements 1 and 2 only are correct.

CStatements 2 and 3 only are correct.

DAll three statements are correct.

Solution & Explanation:Statement 1 is true because repeated outputs are allowed. Statement 2 is true by definition. Statement 3 is false because only one-to-one functions have inverses that are also functions.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard F-IF.1 (Select the correct use of mapping diagrams, tables, graphs, and the vertical line test to decide whether a relation is a function. Associated source-listed standards: CCSS F-IF.1; CA CCSSM F-IF.1; MA 2017 F-IF.1; NY NGLS F-IF.1; TX TEKS Algebra II: §111.40.).