Graph Analysis Worksheet Evidence Analysis Report
Topic: Identifying Functions via Vertical Line Test
Agent:
Date:
Protocol: Apply the Vertical Line Test (VLT). Determine if the graph represents a function. Circle your conclusion and provide your reasoning.
GRAPH #01
Function Identification
Function
Not a Function
Reasoning & Proof:
GRAPH #02
Function Identification
Function
Not a Function
Reasoning & Proof:
GRAPH #03
Function Identification
Function
Not a Function
Reasoning & Proof:
GRAPH #04
Function Identification
Function
Not a Function
Reasoning & Proof:
GRAPH #05
Function Identification
Function
Not a Function
Reasoning & Proof:
GRAPH #06
Function Identification
Function
Not a Function
Reasoning & Proof:
Forensic Lab Lesson Plan Function Forensic Lab
Lesson Plan: Is it a Function?
TIER 1 CLASSROOM
Duration
65 Minutes
Audience
9th Grade Algebra
Objective
Identify functions and relations using the vertical line test on graphs.
The Mission
"Understanding functions is fundamental to advanced mathematics. This lesson provides a crucial visual tool to identify functions, simplifying complex concepts and enabling students to interpret graphs effectively in real-world contexts."
Teacher Preparation
• Review the Slide Deck and familiarize yourself with the coordinate plane examples.
• Print and cut the Vertical Line Test Sort Activity cards (one set per small group).
• Prepare copies of the Graph Analysis Worksheet and Exit Ticket.
• Ensure projector is configured for the visual demonstration.
Evidence Kit (Materials)
Function Slide Deck
Vertical Line Test Sort Cards
Graph Analysis Worksheet
Exit Ticket: Function Check-Up
Instructional Procedure
Hook
10m
What's the Rule?
Display a simple relation (coordinate pairs or graph) that is a function vs. one that is not. Don't label them yet.
"What do you notice about these two relationships? Do they seem different?"
Introduce the Function: A special relationship where each input has exactly ONE output.
Learn
15m
The Vertical Line Test Unveiled
Use the slide deck to define: relation, function, domain, and range.
"If any vertical line intersects the graph at more than one point, then the graph does not represent a function."
Emphasize the why : one x-value (input) cannot lead to two different y-values (outputs) in a function.
Practice
15m
Sorting It Out
Small groups use the Vertical Line Test Sort Cards .
Sort into "Functions" and "Not Functions".
Teacher circulates, checking for common misconceptions (e.g., horizontal lines vs. vertical lines).
Share-back: Groups justify their reasoning for the "Sideways Parabola" card.
Solve
15m
Graph Analysis Challenge
Students work independently on the Graph Analysis Worksheet . Encourage them to draw physical vertical lines through the graphs to 'prove' their findings.
Assess
10m
Function Check-Up
Quick recap discussion on the most difficult graphs. Distribute Exit Ticket for individual mastery check.
Plot Twists Exit Ticket Exit Ticket: Function Check
Final Case Review • Is it a Function?
Agent Name
Date
1
Which of the following best describes a function?
A relation where each output has exactly one input.
A relation where each input has exactly one output.
Any set of ordered pairs.
A graph that always passes through the origin.
2
If a vertical line intersects a graph at two points, what does that tell you?
The graph represents a function.
The graph does NOT represent a function.
The graph is a straight line.
The graph has a positive slope.
3
Sketch a graph that IS a function and explain why.
Sketch Area
Reasoning:
4
Sketch a graph that is NOT a function and explain why.
Sketch Area
Reasoning:
Case Closed
Function Detective Slide Deck Unit: Algebra Essentials
Is it a Function?
The Vertical Line Test Case Files
Subject: 9th Grade Mathematics
What is a Relation?
A relation is a set of ordered pairs.
Shows a relationship between two sets of data (input and output).
Represented as tables, lists of points, or graphs.
Evidence Example
{(1, 2), (3, 4), (5, 6)}
What is a Function?
A function is a special type of relation where each input (x-value) has exactly one output (y-value).
One Input, One Job!
Domain & Range
DOMAIN
The "X" Files
All possible input values (x-values) of a relation or function.
RANGE
The "Y" Factor
All possible output values (y-values) of a relation or function.
The Vertical Line Test (VLT)
A quick visual way to check if a graph represents a function.
RULE: If any vertical line intersects the graph at MORE THAN ONE point, then the graph is NOT a function.
NOT A FUNCTION
Example 1
Investigation
Is this graph a function?
Apply the Vertical Line Test. Imagine scanning a ruler across the grid.
Example 1: Solved
Case Closed
YES!
This is a function.
No matter where you draw a vertical line, it only hits the graph in exactly one point.
Example 2
Investigation
Is this graph a function?
Think carefully. Does any x-value have more than one y-value?
Example 2: Solved
Evidence Logged
NO!
This is NOT a function.
A vertical line crosses the circle at two points. This means one input has two different outputs!
Quick Briefing
1
What is the golden rule for a function?
"Each input has exactly one output."
2
How do we use the Vertical Line Test?
"If a vertical line hits the graph more than once, it's NOT a function."
Prepare for Field Sort Activity...
Vertical Line Test Sort Activity VLT Card Sort
Case Evidence Classification
Confidential
Archive: Alg1-01
Agent Instructions: Cut cards along dashed lines. Apply the Vertical Line Test (VLT) to each. Sort into Functions and Not Functions.
Evid #01
Linear Relation
Evid #02
Quadratic Relation
Evid #03
Circular Relation
Evid #04
Vertical Relation
Evid #05
Root Relation
Evid #06
Cubic Relation
Evid #07
Lateral Quadratic
Evid #08
Absolute Relation
Graph Analysis Answer Key Answer Key
Graph Analysis: Evidence Analysis Report
Teacher Resource
Protocol: Secure Document
GRAPH #01
Identification
Function
Not a Function
Reasoning:
This linear graph passes the Vertical Line Test. Every vertical line drawn will intersect the graph at exactly one point. For every input (x), there is only one output (y).
GRAPH #02
Identification
Function
Not a Function
Reasoning:
This ellipse fails the Vertical Line Test. A vertical line (like x=40) intersects the graph at two distinct points. This means one input has multiple outputs.
GRAPH #03
Identification
Function
Not a Function
Reasoning:
This sideways V-shape fails the VLT. Vertical lines to the right of the vertex (50, 50) intersect the graph twice, proving it is not a function.
GRAPH #04
Identification
Function
Not a Function
Reasoning:
This cubic-style curve passes the VLT. No matter where a vertical line is placed, it only crosses the curve once, making it a valid function.
GRAPH #05
Identification
Function
Not a Function
Reasoning:
This semi-circle (opening downwards) is a function. Any vertical line within the domain [20, 80] intersects only once at the bottom curve.
GRAPH #06
Identification
Function
Not a Function
Reasoning:
This scatter plot represents a function. Each distinct x-value has exactly one corresponding y-value point. No points share the same x-coordinate.
VLT Card Sort Solution Key Classification Guide
Vertical Line Test Sort Activity Solutions
Teacher Key
Archive Reference: Alg1-01-KEY
Classification Summary
Evidence ID Result Quick Justification Evid #01 FUNCTION Linear: Passess VLT everywhere. Evid #02 FUNCTION Quadratic: Passes VLT everywhere. Evid #03 NOT A FUNCTION Circular: Fails VLT (2 intersections). Evid #04 NOT A FUNCTION Vertical Line: Infinite points on one x. Evid #05 FUNCTION Root: Passes VLT across domain. Evid #06 FUNCTION Cubic: Passes VLT everywhere. Evid #07 NOT A FUNCTION Sideways Parabola: Fails VLT. Evid #08 FUNCTION Absolute Value: Passes VLT everywhere.
Teaching Points & Misconceptions
The Vertical Exception: Evidence #04 is the "ultimate fail" for the VLT. Remind students that a single vertical line contains an infinite number of points, all sharing the same x-value.
Curvature: In Evidence #07, students often confuse it with a standard parabola (#02). Emphasize that direction matters—standard parabolas pass the VLT, sideways ones do not.
Discrete vs. Continuous: While this activity focuses on continuous lines/curves, use the Answer Key visual from the worksheet (Graph #06) to discuss how discrete points also follow the same rules.
