Printable Relations & Functions Worksheet | Grade 10 Math

This worksheet provides essential practice for high school math students learning to distinguish between relations and functions. Through 21 targeted problems, learners will solidify their understanding of this foundational algebra concept by analyzing tables, graphs, mapping diagrams, and sets of ordered pairs to determine if a relation is a function.

At a Glance

• Grade: 10 (adaptable for 9-11) · Subject: Algebra / Math
• Standard: CCSS.MATH.CONTENT.HSF-IF.A.1 — Understand that a function assigns each input to exactly one output.
• Skill Focus: Identifying Functions
• Format: 4 pages · 21 problems · Answer key included · PDF
• Best For: In-class practice or homework
• Time: 25–40 minutes

What's Inside

This resource contains a three-page worksheet and a one-page answer key for easy grading. The 21 problems are varied to ensure comprehensive understanding, covering relations presented as sets of ordered pairs, input-output tables, mapping diagrams, and graphs. The clean layout allows students to focus on the skill.

Skill Progression

The worksheet follows a logical progression that supports learning through a gradual release of responsibility.

• Guided Practice: The first section (9 problems) asks students to evaluate simple relations from tables and ordered pairs, establishing the core "one input, one output" rule.
• Supported Practice: The second section (6 problems) introduces mapping diagrams, a visual scaffold to help students trace inputs to outputs.
• Independent Practice: The final section (6 problems) challenges students to apply the vertical line test to various graphs independently.

This structure ensures students build confidence as they move from basic identification to graphical application.

Standards Alignment

This worksheet is directly aligned with Common Core standard CCSS.MATH.CONTENT.HSF-IF.A.1, which requires students to understand that a function assigns each input to exactly one output. The tasks provide the varied practice needed to master this concept. The standard code can be copied directly into lesson plans, IEP goals, or curriculum maps.

How to Use It

Use this worksheet for in-class practice after a lesson on functions, or assign it as homework for reinforcement. As a formative assessment, use the final page as a quick check for understanding of the vertical line test. Circulate to spot misconceptions while students work. Most students will complete all 21 problems in 25 to 40 minutes.

Who It's For

This resource is designed for students in Grades 9-11 studying Algebra 1. It is ideal for learners needing clear, focused practice on a single concept. For struggling students, pre-teach the vertical line test with an anchor chart. This worksheet pairs well with a follow-up lesson on function notation and evaluating functions.

Mastering the distinction between relations and functions is a gateway to higher-level mathematics. This worksheet provides targeted practice on standard CCSS.MATH.CONTENT.HSF-IF.A.1, ensuring students understand a function assigns each domain element to exactly one range element. This skill is essential for working with linear equations and beyond. The NAEP reports that proficiency in functions is a key indicator of college readiness. By providing 21 problems across multiple representations (tables, ordered pairs, graphs), this resource helps build robust understanding. It provides the focused repetition that research from Fisher & Frey (2014) shows is crucial for moving new knowledge into long-term memory, making abstract algebraic concepts concrete and manageable.