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Identifying Graphs of Functions Worksheet | Vertical Line 91¶¶Ňőt | Algebra 1

Identifying Graphs of Functions Worksheet | Vertical Line 91¶¶Ňőt | Algebra 1

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

11 August 2026

pdf, 158.37 KB
pdf, 158.37 KB

A worksheet on identifying whether a given graph represents a function. Answers are included.

Master the vertical line test with this ready-to-print math worksheet. Includes full worked solutions for 14 varied graphs to help students identify functions confidently.

Help your students master the vertical line test and identify functions from graphs with ease!
Visually distinguishing between functions and relations is a core skill in secondary math curricula, including GCSE, IGCSE, and foundational algebra tracks. While the concept seems straightforward, students frequently struggle when presented with non-standard curves, vertical lines, or closed shapes like circles and ellipses. This structured worksheet bridges that gap, offering extensive practice to build mathematical fluency.

Mathematical Concept Definition
What is the vertical line test? The vertical line test is a visual method used to determine if a curve on a graph represents a function. A relation is a function if and only if no vertical line intersects its graph more than once. If any vertical line passes through two or more points on the graph, the relation fails the test and is not a function because a single input (x-value) maps to multiple outputs (y-values).

What is Included in This Resource?
• 14 Progressive Graphs: Over three pages of high-quality coordinate grids featuring a diverse mix of mathematical relations.
• Diverse Curve Types: Exercises cover standard linear functions, parabolas, cubic curves, sideways parabolas, circles, ellipses, and rational function graphs.
• Step-by-Step Solutions: A complete three-page answer key featuring a clear “This is a function” or “This is not a function” label under every single graph. This makes it ideal for rapid teacher grading or student self-assessment.

Specific Graph Types and Misconceptions Challenged

  1. Linear and Polynomial Functions: Standard straight lines, upward and downward parabolas, and cubic curves where students see functions in action.
  2. Special Lines: Incorporates a vertical line graph to test understanding of undefined slopes and function rules.
  3. Closed Conic Sections: Includes circles and ellipses to clearly illustrate relations that fail the vertical line test.
  4. Sideways Curves: Features a sideways parabola and an S-curve to ensure students are actively drawing vertical lines rather than guessing.

Perfect For Classroom Use As:
• A main independent practice worksheet during algebra and graphing lessons
• Homework assignments or consolidation tasks
• Retrieval practice, revision, or exam preparation
• Comprehensive substitute teacher (cover lesson) plans

Get this resource as part of a bundle and save up to 54%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

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