Mapping Diagrams Guided Handout Algebra Foundations • Guided Practice
Mapping Diagrams & Functions
Name:
Date:
Period:
Core Concepts: Relations & Mapping Diagrams
Input / Domain (\(x\))
The set of all first coordinates or independent values. Shown in the left bubble . Never repeat a value!
Output / Range (\(y\))
The set of all second coordinates or dependent values. Shown in the right bubble . Never repeat a value!
The Function Test
A relation is a function if each input has exactly one output. In a mapping diagram: Exactly 1 arrow leaves each input!
MODEL 1
Coordinate Pairs → Mapping Diagram & Function Check
Step-by-Step Worked Example
Given the relation: \(R = \{(-2, 3), (0, 5), (2, 3), (4, -1)\}\)
1
List unique inputs in order: Domain = \{-2, 0, 2, 4\}
2
List unique outputs in order: Range = \{-1, 3, 5\} (Notice 3 appears once!)
3
Draw directional arrows: From each \(x\) to its paired \(y\).
✓
Is it a function? YES. Each input has only 1 arrow pointing outward. Multiple arrows arriving at output \(3\) is totally fine!
Domain (x) -2 0 2 4 Range (y) -1 3 5
TRY IT 1
Translate Table → Create Mapping → Check Function
Complete with a partner or independently
Analyze the table below. Write unique values in order inside each bubble, draw the arrows, and answer the questions.
Input (\(x\))
Output (\(y\))
3
7
-1
4
3
10
5
4
⚠ Look closely at the \(x\)-values!
Draw Your Mapping Diagram Here Domain (x) Range (y)
Domain:
Range:
Is this relation a function?
YES NO
Explain your reason using arrows:
Golden Arrow Rule: To test for a function, count arrows leaving each input . If ANY input branches into 2 or more arrows, it is NOT a function!
Page 1 of 2
Deepening Understanding
Interpreting & Converting Mappings
Mapping Diagrams Mastery
1 2 3 8 9
IS A FUNCTION
Every input sends out exactly 1 arrow . Multiple inputs sharing an output is completely allowed!
4 7 -2 0 5
NOT A FUNCTION
Input 4 branches into 2 arrows (outputs \(-2\) and \(0\)). One input has multiple outputs!
MODEL 2
Reading a Mapping Diagram → Writing Ordered Pairs & Table
x -4 1 3 y 2 6 8
How to Trace: Follow each arrow starting from its input to its destination output. Each arrow represents exactly one ordered pair \((x, y)\).
Set of Ordered Pairs:
{(-4, 2), (1, 8), (3, 6)}
Domain & Range:
Domain: \{-4, 1, 3\}
Range: \{2, 6, 8\}
TRY IT 2
Interpret Diagram & Build Representations
Your Turn
Domain -5 0 6 Range -2 4
Write Ordered Pairs:
Complete Table:
Domain:
Range:
Function? (Yes/No & Why):
Common Misconception Alert • Error Analysis
Student Claim: Marcus says: "The relation in Try It 2 cannot be a function because both inputs \(-5\) and \(6\) point to the same output \(-2\)."
Is Marcus correct? Critique his reasoning below:
Tip: If every input has one single arrow exiting, you've got a function! Page 2 of 2
Mapping Diagrams Practice Worksheet Independent Practice
Mapping Diagrams Mastery Worksheet
Name:
Date:
Score:
PART 1
Construct Mapping Diagrams • State Domain & Range
For each relation below, write unique inputs and outputs inside each bubble (least to greatest), draw directional arrows from input to output, and state whether the relation is a function.
1. Relation \(A\):
\{(1, 4), (2, -3), (3, 4), (5, 0)\}
Domain:
Range:
Domain Range
Function?
Yes No
Why / Why not?
2. Table of Values:
\(x\)
\(y\)
-2
5
0
1
3
-4
-2
9
Domain:
Range:
Domain Range
Function?
Yes No
Why / Why not?
3. Relation \(C\):
\{(-4, 2), (-1, 2), (0, 2), (6, 2)\}
Domain:
Range:
Domain Range
Function?
Yes No
Why / Why not?
PART 2
Interpret Mapping Diagrams • Extract Ordered Pairs
4. Diagram \(M_1\) Trace all arrows
-3 0 5 1 7
Ordered Pairs:
Function? [ ] Yes [ ] No
Arrows per input:
5. Diagram \(M_2\) Trace all arrows
2 4 -1 3 8
Ordered Pairs:
Function? [ ] Yes [ ] No
Problem input:
Remember: Never repeat values inside the Domain or Range bubbles! Page 1 of 2
Advanced Practice & Synthesis
Function Detective & Mixed Representations
Algebra 1 • Unit: Relations
PART 3
Function Detective: Inspect, Classify & Justify
Determine if each mapping diagram represents a function. State your mathematical reason using the behavior of the arrows leaving the inputs.
-2 1 4 6 10 14
Diagram A
Function Not a Function
Reason:
3 8 0 5 11
Diagram B
Function Not a Function
Reason:
-4 0 4 16
Diagram C
Function Not a Function
Reason:
5 9 2 8
Diagram D
Function Not a Function
Reason:
PART 4
Multi-Representation Bridge
Complete the missing representations for the relation described below.
1. Ordered Pairs (Given)
\{(-3, 1), (-1, 0), (2, 4), (4, 1)\}
Domain:
Range:
2. Complete Table
Input (\(x\))
Output (\(y\))
3. Create Mapping Domain Range Is it a function? [ ] Yes [ ] No
Real-World Scenario: The Vending Machine Function
A snack vending machine maps button codes (input: e.g., A1, B2, C3) to snack prices in dollars (output: e.g., $1.50, $2.00).
Scenario A:
Two different buttons (A1 and B2) both cost $1.50. Does this violate the definition of a function? Why or why not?
Scenario B:
Pressing button C3 could charge either $1.25 or $2.50 randomly. Is this a function? How would its mapping look?
Unit: Relations & Functions • Independent Practice Complete Page 2 of 2
Mapping Diagrams Solutions Guide Teacher Key & Solutions
Guided Handout Answer Key
COMPLETE SOLUTIONS
Handout Page 1 • Try It 1 Solution NOT A FUNCTION
x -1 3 5 y 4 7 10
Domain: \{-1, 3, 5\} (3 is written once only)
Range: \{4, 7, 10\} (4 is written once only)
Is it a function? NO.
Key Explanation: The input 3 has two outgoing arrows pointing to two different outputs (\(7\) and \(10\)). A function requires exactly one output per input.
Handout Page 2 • Try It 2 & Error Analysis Solution IS A FUNCTION
Ordered Pairs: {(-5, -2), (0, 4), (6, -2)}
Table Values: \((-5, -2)\), \((0, 4)\), \((6, -2)\)
Domain: \{-5, 0, 6\}
Range: \{-2, 4\}
Is it a function? YES. Each input has exactly one arrow exiting.
Marcus Critique (Error Analysis):
Marcus is INCORRECT. A relation is still a function when multiple inputs share the same output (many-to-one). The strict rule applies only to inputs: each input must map to at most one output. Two arrows arriving at \(-2\) is valid!
Instructional Strategies & Common Student Traps
Duplicate Values Trap
Students often write repeated numbers in the bubble (e.g., writing 3 twice). Enforce: A bubble is a mathematical set; sets never repeat members!
Arrow Direction Confusion
Students sometimes count arrows entering an output instead of arrows leaving an input. Reiterate: Look ONLY at the domain bubble to test for a function.
Vending Machine Analogy
Use the snack machine: Multiple buttons giving you the same chip brand is normal (function). One button giving you unpredictable items is broken (not a function)!
Teacher Solutions Guide • Mapping Diagrams Page 1 of 2
Teacher Key & Solutions
Independent Practice Solutions
Worksheet Pages 1 & 2
Part 1 • Constructing Mapping Diagrams Solutions
Problem 1 (Relation A)
Domain: \{1, 2, 3, 5\}
Range: \{-3, 0, 4\}
Function? YES.
Each input has 1 arrow. Both 1 and 3 map to 4, which is allowed.
Problem 2 (Table)
Domain: \{-2, 0, 3\}
Range: \{-4, 1, 5, 9\}
Function? NO.
Input \(-2\) maps to both \(5\) and \(9\) (2 outgoing arrows).
Problem 3 (Relation C)
Domain: \{-4, -1, 0, 6\}
Range: \{2\}
Function? YES.
Constant function. 4 inputs all point to single output 2.
Part 2 • Extracting Relations & Part 3 • Function Detective
Part 2: Problems 4 & 5
Problem 4: Pairs: {(-3, 1), (0, 7), (5, 7)}. Function: YES (1 arrow per input).
Problem 5: Pairs: {(2, -1), (2, 3), (4, 8)}. Function: NO (Input 2 branches to -1 and 3).
Part 3: Detective A – D
Diag A: Function (1-to-1, exactly 1 arrow per input).
Diag B: Not a Function (Input 3 branches to 0 and 5).
Diag C: Function (Many-to-1, all inputs map to 16).
Diag D: Not a Function (Both 5 and 9 branch to 2 outputs).
Part 4 & 5 • Multi-Representation & Vending Machine
Part 4: Multi-Representation Bridge
Domain: \{-3, -1, 2, 4\}
Range: \{0, 1, 4\}
Table entries: \((-3, 1)\), \((-1, 0)\), \((2, 4)\), \((4, 1)\)
Mapping check: Arrows from \(-3 \to 1\), \(-1 \to 0\), \(2 \to 4\), \(4 \to 1\).
Function? YES (Each input has 1 arrow).
Part 5: Real-World Scenario Answers
Scenario A: No violation. Different buttons (inputs A1 and B2) can share the same price ($1.50). Each button still has only one set price.
Scenario B: NOT a function. Input C3 would have 2 arrows branching to $1.25 and $2.50. A customer does not know what they will be charged!
Quick Grading Rubric (Total: 25 Points)
Part 1 (9 pts): 3 pts each (1 pt bubble sets, 1 pt arrows, 1 pt function + reason).
Part 2 (4 pts): 2 pts each (1 pt coordinate pairs, 1 pt function ID).
Part 3 (6 pts): 1.5 pts each (0.5 pt classification, 1 pt valid arrow justification).
Part 4 & 5 (6 pts): 3 pts multi-rep bridge, 3 pts real-world reasoning.
Unit: Relations & Functions • Independent Practice Complete Solutions Page 2 of 2
