Function Features Review Worksheet Algebra 1 Relations & Functions Unit
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Function Features Review
Master core relation vocabulary, input-output behaviors, and domain & range rules.
Name:
Date:
Period:
1 Part 1: Key Terms Matching
Match each term with its exact definition.
A. Domain B. Range C. Independent Variable D. Dependent Variable E. Function
The output or \(y\)-values of a relation.
A relation where each input has exactly ONE output (NO repeating \(x\)-values!).
An ordered list of \(x\)-values of a relation, ex. \(D: \{1, 3, 5, 17\}\).
The input or \(x\)-values of a relation.
An ordered list of \(y\)-values of a relation, ex. \(R: \{-4, 2, 12\}\).
2 Part 2: Domain, Range & Variables in Practice
List values in numerical order without duplicates.
Problem A: Ordered Pairs Set Notation
Relation \(Q = \{(-3, 4), (1, -2), (5, 9), (-3, 0), (7, 4)\}\)
Domain (\(D\)):
D = { }
Range (\(R\)):
R = { }
Is \(Q\) a function? Yes No
Problem B: Real-World Variables Context Analysis
"The total electric bill (\(C\), in dollars) charged by the power company depends on the amount of electricity used (\(k\), in kilowatt-hours)."
Independent Variable (Input / \(x\)):
Dependent Variable (Output / \(y\)):
Which variable causes the other to change?
3 Part 3: Function Detective — Check Your Inputs
Golden Rule: Each input must map to exactly ONE output!
Relation Table 1
Function Not a Function
<table class="w-full text-xs text-center border-collapse border border-slate-300 mb-2 font-mono"><tbody><tr class="bg-slate-100 font-semibold"><td class="border border-slate-300 py-1 w-1/5">\(x\) (Input)</td><td class="border border-slate-300 py-1">2</td><td class="border border-slate-300 py-1">4</td><td class="border border-slate-300 py-1">6</td><td class="border border-slate-300 py-1">8</td></tr><tr><td class="border border-slate-300 py-1 bg-slate-50 font-semibold">\(y\) (Output)</td><td class="border border-slate-300 py-1">7</td><td class="border border-slate-300 py-1">7</td><td class="border border-slate-300 py-1">11</td><td class="border border-slate-300 py-1">15</td></tr></tbody></table>
Justify your answer:
Relation Table 2
Function Not a Function
<table class="w-full text-xs text-center border-collapse border border-slate-300 mb-2 font-mono"><tbody><tr class="bg-slate-100 font-semibold"><td class="border border-slate-300 py-1 w-1/5">\(x\) (Input)</td><td class="border border-slate-300 py-1">1</td><td class="border border-slate-300 py-1">3</td><td class="border border-slate-300 py-1">5</td><td class="border border-slate-300 py-1 text-red-600 font-bold">3</td></tr><tr><td class="border border-slate-300 py-1 bg-slate-50 font-semibold">\(y\) (Output)</td><td class="border border-slate-300 py-1">10</td><td class="border border-slate-300 py-1">14</td><td class="border border-slate-300 py-1">18</td><td class="border border-slate-300 py-1 text-red-600 font-bold">22</td></tr></tbody></table>
Justify your answer:
Core Rule A relation can repeat \(y\)-values and still be a function, but repeating \(x\)-values with different \(y\)-values is forbidden !
Turn page for Part 4 →
Algebra 1
Function Features Review: Graphs & Models
Name:
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4 Part 4: Discrete vs. Continuous Relations
Determine whether points are isolated or connected.
Graph Model A
Discrete Continuous
Define Discrete (what does it contain?):
Graph Model B
Discrete Continuous
Define Continuous (how is it connected?):
5 Part 5: Linear vs. Non-Linear Patterns
Examine tables and equations for constant slopes and exponent rules.
Analyzing Tables (Pattern Detection)
Table X:
Linear Non-linear
<table class="w-full text-center border border-slate-300 font-mono text-[10px]"><tbody><tr class="bg-slate-100"><td class="border border-slate-300 py-0.5">\(x\)</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td class="border border-slate-300 bg-slate-50 py-0.5">\(y\)</td><td>3</td><td>7</td><td>11</td><td>15</td></tr></tbody></table>
Table Y:
Linear Non-linear
<table class="w-full text-center border border-slate-300 font-mono text-[10px]"><tbody><tr class="bg-slate-100"><td class="border border-slate-300 py-0.5">\(x\)</td><td>1</td><td>2</td><td>3</td><td>4</td></tr><tr><td class="border border-slate-300 bg-slate-50 py-0.5">\(y\)</td><td>3</td><td>9</td><td>27</td><td>81</td></tr></tbody></table>
Analyzing Equations (Exponents & Denominators)
Classify each equation based on vocabulary rules:
\(y = 4x - 9\)
Linear Non-linear
\(y = x^2 + 5\)
Linear Non-linear
\(y = \frac{8}{x}\)
Linear Non-linear
6 Part 6: The Vertical Line Test
Check if any vertical line touches more than once.
Graph 1: Circle Relation
Function Not a Function
Explain using the Vertical Line Test rule:
Graph 2: V-Shape (Absolute Value)
Function Not a Function
Explain using the Vertical Line Test rule:
Summary Check: Fill in the Blanks
1. A function that forms a straight line when graphed:
2. Equations with exponents or radicals are:
Function Features Quiz Quiz Algebra 1 • Relations & Functions
Score: / 20
Function Features Quiz
Demonstrate mastery of relation vocabulary, representations, and function rules.
Name:
Date:
Period:
A Part A: Terminology Match (1 pt each • 5 pts)
Write the letter of the matching vocabulary word on the blank.
A. Domain
B. Range
C. Independent Var.
D. Dependent Var.
E. Function
The output or \(y\)-values of a relation.
A relation where each input has exactly ONE output (NO repeating \(x\)-values!).
The ordered list of \(x\)-values of a relation (e.g., \(D: \{1, 3, 5, 17\}\)).
The input or \(x\)-values of a relation.
The ordered list of \(y\)-values of a relation (e.g., \(R: \{-4, 2, 12\}\)).
B Part B: Conceptual Multiple Choice (2 pts each • 6 pts)
Select the single best answer for each question.
6. Which method is used to determine if a graph is a function by checking if vertical lines share points?
A) Horizontal Line Test B) Vertical Line Test C) Coordinate Axis Test D) Slope-Intercept Test
7. A scatterplot contains only individual, disconnected dots. How is this relation categorized?
A) Continuous B) Discrete C) Non-linear Curve D) Undefined
8. Which algebraic equation represents a linear function?
A) \(y = 3x^2 - 1\) B) \(y = \frac{6}{x}\) C) \(y = -2x + 7\) D) \(y = \sqrt{x} + 4\)
C Part C: Application & Analysis (3 pts each • 9 pts)
Provide complete mathematical responses in the designated spaces.
9. Set Analysis
Given relation \(M\):
\(\{(-4, 3), (0, 7), (2, 3), (5, -1)\}\)
Domain (\(D\)):
D = { }
Range (\(R\)):
R = { }
Function? Yes No
10. Graphical Test
Examine the graph below:
Function? Yes No
Why? (Vertical Line Test rule):
11. Pattern Analysis
Examine the table pattern:
<table class="w-full text-center border border-slate-300 font-mono text-[10px] mb-1.5"><tbody><tr class="bg-slate-100"><td class="border border-slate-300 py-0.5">\(x\)</td><td>1</td><td>2</td><td>3</td><td>4</td></tr><tr><td class="border border-slate-300 bg-slate-50 py-0.5">\(y\)</td><td>5</td><td>10</td><td>20</td><td>40</td></tr></tbody></table>
Function Features Answer Key Answer Key Teacher Reference • Review Worksheet
Worksheet Solutions
Review Worksheet Key
Solutions and instructional notes for parts 1 through 7 of the review packet.
Course: Algebra 1
Part 1: Key Terms Matching 5 items
D (Dep. Var)
E (Function)
A (Domain)
C (Indep. Var)
B (Range)
Part 2: Domain, Range & Variables
Problem A (Ordered Pairs)
Domain: D = {-3, 1, 5, 7} (write -3 once)
Range: R = {-2, 0, 4, 9} (write 4 once, in order)
Function? No — Input \(-3\) repeats with outputs \(4\) and \(0\).
Problem B (Real-World Variables)
Independent Variable: Electricity used (\(k\), kWh)
Dependent Variable: Electric bill cost (\(C\), $)
Causality: Kilowatt-hours used causes/determines the cost.
Part 3: Function Detective
Table 1: Function
Each input (\(2, 4, 6, 8\)) has exactly ONE output. Outputs may repeat (\(y=7\)), but inputs do not repeat.
Table 2: Not a Function
The input \(x = 3\) repeats with two different outputs (\(14\) and \(22\)), violating the function definition.
Part 4: Discrete / Continuous
Model A: Discrete (only isolated points).
Model B: Continuous (connected straight line or curve).
Part 5: Linear / Non-Linear
Table X: Linear (+4 slope)
Table Y: Non-linear (\(\times 3\) pattern)
\(y = 4x - 9\): Linear (straight line)
\(y = x^2 + 5\): Non-linear (exponent)
\(y = \frac{8}{x}\): Non-linear (\(x\) denominator)
Part 6 & 7: VLT & Summary
Circle: Not a Function (shares vertical points)
V-Shape: Function (passes VLT)
1. Straight line = Linear
2. Exponents/radicals = Non-linear
Teaching Strategy: Have students highlight all \(x\)-values in yellow. If they see two identical yellow numbers with different outputs, it is immediately not a function! Page 1 of 2
Function Mastery Quiz Quiz • Form B Algebra 1 • Relations & Functions
Score: / 20
Function Mastery Quiz
Demonstrate mastery of relation vocabulary, representations, and function rules.
Name:
Date:
Period:
A Part A: Terminology Match (1 pt each • 5 pts)
Write the letter of the matching vocabulary word on the blank.
A. Domain
B. Range
C. Independent Var.
D. Dependent Var.
E. Function
The ordered list of \(y\)-values of a relation (e.g., \(R: \{-4, 2, 12\}\)).
The input or \(x\)-values of a relation.
The ordered list of \(x\)-values of a relation (e.g., \(D: \{1, 3, 5, 17\}\)).
The output or \(y\)-values of a relation.
A relation where each input has exactly ONE output (NO repeating \(x\)-values!).
B Part B: Conceptual Multiple Choice (2 pts each • 6 pts)
Select the single best answer for each question.
6. A graph consists of an unbroken, connected curved line with no gaps. Which term describes this relation?
A) Discrete B) Continuous C) Isolated Relation D) Scatterplot
7. If a vertical line passes through two points on a graphed relation, what conclusion must be made?
A) The graph is a linear function B) The relation is NOT a function C) The relation has no range values D) The graph is discrete
8. Which algebraic equation represents a non-linear function?
A) \(y = 5x - 3\) B) \(y = \frac{1}{2}x + 6\) C) \(y = x^2 - 7\) D) \(y = -4x\)
C Part C: Application & Analysis (3 pts each • 9 pts)
Provide complete mathematical responses in the designated spaces.
9. Set Analysis
Given relation \(K\):
\(\{(-1, 4), (0, 4), (3, 8), (6, -2)\}\)
Domain (\(D\)):
D = { }
Range (\(R\)):
R = { }
Function? Yes No
10. Graphical Test
Examine the graph below:
Function? Yes No
Why? (Vertical Line Test rule):
11. Pattern Analysis
Examine the table pattern:
<table class="w-full text-center border border-slate-300 font-mono text-[10px] mb-1.5"><tbody><tr class="bg-slate-100"><td class="border border-slate-300 py-0.5">\(x\)</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td class="border border-slate-300 bg-slate-50 py-0.5">\(y\)</td><td>4</td><td>9</td><td>14</td><td>19</td></tr></tbody></table>
Function Mastery Answer Key Answer Key Function Mastery Quiz • Form B Key
Total: 20 Points
Function Mastery Answer Key
Complete solutions, grading criteria, and point values for the Form B vocabulary quiz.
Course: Algebra 1
Part A: Terminology Match (5 Points • 1 pt each)
Item 1 B Range
Item 2 C Independent Var
Item 3 A Domain
Item 4 D Dependent Var
Item 5 E Function
Part B: Multiple Choice (6 Points • 2 pts each)
Question 6 B
Continuous: An unbroken curve or line with connected values and no gaps.
Question 7 B
Not a function: Fails the Vertical Line Test because it shares points vertically.
Question 8 C
\(y = x^2 - 7\): Non-linear because it contains an exponent (\(x^2\)).
Part C: Applied Problem Solving (9 Points • 3 pts each)
9. Set Analysis (3 pts)
Domain (1 pt): {-1, 0, 3, 6}
Range (1 pt): {-2, 4, 8}
Function? (1 pt): Yes
Note: List in ascending order. Value 4 written only once.
10. Graphical Test (3 pts)
Function? (1 pt): Yes
Explanation (2 pts): Passes the Vertical Line Test; every vertical line touches the S-curve at at most one point (does not share points vertically).
Give 1 pt if they state "passes VLT" without full explanation.
11. Pattern Analysis (3 pts)
Type (1 pt): Linear
Explanation (2 pts): Has a consistent addition pattern / constant rate of change (\(+5\) for each step of \(+1\) in \(x\); constant slope \(m = 5\)).
Consistent addition = linear slope.
Form A vs. Form B Comparison (Equivalency Table)
<table class="w-full text-center border border-indigo-200 font-mono text-[10px] bg-white"><tbody><tr class="bg-indigo-100/70 font-semibold text-indigo-950 font-sans"><td class="border border-indigo-200 py-1">Concept Tested</td><td class="border border-indigo-200 py-1">Form A (Features Quiz)</td><td class="border border-indigo-200 py-1">Form B (Mastery Quiz)</td></tr><tr><td class="border border-indigo-200 py-0.5 text-left px-2 font-sans">Matching 1-5</td><td class="border border-indigo-200 py-0.5">D, E, A, C, B</td><td class="border border-indigo-200 py-0.5">B, C, A, D, E</td></tr><tr><td class="border border-indigo-200 py-0.5 text-left px-2 font-sans">Discrete / Continuous</td><td class="border border-indigo-200 py-0.5">Q7: Discrete points (B)</td><td class="border border-indigo-200 py-0.5">Q6: Continuous curve (B)</td></tr><tr><td class="border border-indigo-200 py-0.5 text-left px-2 font-sans">Vertical Line Test</td><td class="border border-indigo-200 py-0.5">Q10: Circle (Fails / Not Func)</td><td class="border border-indigo-200 py-0.5">Q10: S-Curve (Passes / Func)</td></tr><tr><td class="border border-indigo-200 py-0.5 text-left px-2 font-sans">Table Pattern</td><td class="border border-indigo-200 py-0.5">Q11: Doubling (Non-linear)</td><td class="border border-indigo-200 py-0.5">Q11: Adding 5 (Linear)</td></tr></tbody></table>
