Practice
Relations and Functions Practice
Fifty original multi-representation questions with mappings, tables, coordinate planes, and function notation.
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Question 1
Explanation
Read the ordered pair as horizontal \(x=2\), then vertical \(y=3\). Its signs place it Quadrant I.
Question 2
Explanation
Read the ordered pair as horizontal \(x=-3\), then vertical \(y=2\). Its signs place it Quadrant II.
Question 3
Explanation
Read the ordered pair as horizontal \(x=-4\), then vertical \(y=-1\). Its signs place it Quadrant III.
Question 4
Explanation
Read the ordered pair as horizontal \(x=3\), then vertical \(y=-4\). Its signs place it Quadrant IV.
Question 5
Explanation
Read the ordered pair as horizontal \(x=0\), then vertical \(y=3\). Its signs place it on an axis.
Question 6
Explanation
The domain contains every distinct first coordinate, so it is \(\{1,3,5\}\).
Question 7
Explanation
The domain contains every distinct first coordinate, so it is \(\{-2,0,4\}\).
Question 8
Explanation
The domain contains every distinct first coordinate, so it is \(\{2,6,8\}\).
Question 9
Explanation
The domain contains every distinct first coordinate, so it is \(\{0,2,9\}\).
Question 10
Explanation
The domain contains every distinct first coordinate, so it is \(\{-5,-1,3\}\).
Question 11
Explanation
Inspect the inputs. Each input appears once. Repeated outputs are allowed, so the relation is a function.
Question 12
Explanation
Inspect the inputs. Input \(1\) is paired with both \(1\) and \(4\), so the function rule fails.
Question 13
Explanation
Inspect the inputs. Each input appears once. Repeated outputs are allowed, so the relation is a function.
Question 14
Explanation
Inspect the inputs. Input \(3\) is paired with both \(1\) and \(4\), so the function rule fails.
Question 15
Explanation
Inspect the inputs. Each input appears once. Repeated outputs are allowed, so the relation is a function.
Question 16
Explanation
Every input has exactly one outgoing arrow. Inputs may share outputs, so this mapping is a function.
Question 17
Explanation
Input \(1\) has two outgoing arrows, so it has two outputs and the mapping is not a function.
Question 18
Explanation
Every input has exactly one outgoing arrow. Inputs may share outputs, so this mapping is a function.
Question 19
Explanation
Input \(1\) has two outgoing arrows, so it has two outputs and the mapping is not a function.
Question 20
Explanation
Every input has exactly one outgoing arrow. Inputs may share outputs, so this mapping is a function.
Question 21
Explanation
The range is the set of distinct output values in the \(y\)-column: \(\{2,4,6\}\).
Question 22
Explanation
The range is the set of distinct output values in the \(y\)-column: \(\{3,6,9\}\).
Question 23
Explanation
The range is the set of distinct output values in the \(y\)-column: \(\{4,8,12\}\).
Question 24
Explanation
The range is the set of distinct output values in the \(y\)-column: \(\{5,10,15\}\).
Question 25
Explanation
The range is the set of distinct output values in the \(y\)-column: \(\{6,12,18\}\).
Question 26
Explanation
Substitute \(x=-2\): \(2(-2)+3=-1\).
Question 27
Explanation
Substitute \(x=-1\): \(3(-1)+2=-1\).
Question 28
Explanation
Substitute \(x=0\): \(4(0)+1=1\).
Question 29
Explanation
Substitute \(x=1\): \(5(1)+0=5\).
Question 30
Explanation
Substitute \(x=2\): \(6(2)-1=11\).
Question 31
Explanation
Use parentheses for the input: \(-2^2-2(-2)+3=11\).
Question 32
Explanation
Use parentheses for the input: \(-1^2-2(-1)+3=6\).
Question 33
Explanation
Use parentheses for the input: \(0^2-2(0)+3=3\).
Question 34
Explanation
Use parentheses for the input: \(1^2-2(1)+3=2\).
Question 35
Explanation
Use parentheses for the input: \(2^2-2(2)+3=3\).
Question 36
Explanation
Substitute the entire input: \(2(u+1)-1=2u+1\).
Question 37
Explanation
Substitute the entire input: \(3(u+1)+0=3u+3\).
Question 38
Explanation
Substitute the entire input: \(4(u+1)+1=4u+5\).
Question 39
Explanation
Substitute the entire input: \(5(u+1)+2=5u+7\).
Question 40
Explanation
Substitute the entire input: \(6(u+1)+3=6u+9\).
Question 41
Explanation
Every fixed x-value reaches at most one plotted y-value, so the graph is a function.
Question 42
Explanation
At least one vertical line meets the graph at two points, giving one input two outputs.
Question 43
Explanation
Every fixed x-value reaches at most one plotted y-value, so the graph is a function.
Question 44
Explanation
At least one vertical line meets the graph at two points, giving one input two outputs.
Question 45
Explanation
Every fixed x-value reaches at most one plotted y-value, so the graph is a function.
Question 46
Explanation
Input \(1\) appears twice. A function requires both occurrences to have the same output, so \(c=-2\).
Question 47
Explanation
Input \(1\) appears twice. A function requires both occurrences to have the same output, so \(c=-1\).
Question 48
Explanation
Input \(1\) appears twice. A function requires both occurrences to have the same output, so \(c=0\).
Question 49
Explanation
Input \(1\) appears twice. A function requires both occurrences to have the same output, so \(c=1\).
Question 50
Explanation
Input \(1\) appears twice. A function requires both occurrences to have the same output, so \(c=2\).
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
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Questions to review
No mistakes this time. Excellent work.
- Question 1Coordinate planeEasy
- Question 2Coordinate planeEasy
- Question 3Coordinate planeEasy
- Question 4Coordinate planeEasy
- Question 5Coordinate planeEasy
- Question 6Domain and rangeEasy
- Question 7Domain and rangeEasy
- Question 8Domain and rangeEasy
- Question 9Domain and rangeEasy
- Question 10Domain and rangeEasy
- Question 11Function test from ordered pairsEasy
- Question 12Function test from ordered pairsEasy
- Question 13Function test from ordered pairsEasy
- Question 14Function test from ordered pairsEasy
- Question 15Function test from ordered pairsEasy
- Question 16Function test from mappingMedium
- Question 17Function test from mappingMedium
- Question 18Function test from mappingMedium
- Question 19Function test from mappingMedium
- Question 20Function test from mappingMedium
- Question 21Table representationMedium
- Question 22Table representationMedium
- Question 23Table representationMedium
- Question 24Table representationMedium
- Question 25Table representationMedium
- Question 26Evaluate function notationMedium
- Question 27Evaluate function notationMedium
- Question 28Evaluate function notationMedium
- Question 29Evaluate function notationMedium
- Question 30Evaluate function notationMedium
- Question 31Evaluate quadratic functionMedium
- Question 32Evaluate quadratic functionMedium
- Question 33Evaluate quadratic functionMedium
- Question 34Evaluate quadratic functionMedium
- Question 35Evaluate quadratic functionMedium
- Question 36Substitute an expressionMedium
- Question 37Substitute an expressionMedium
- Question 38Substitute an expressionMedium
- Question 39Substitute an expressionMedium
- Question 40Substitute an expressionMedium
- Question 41Vertical line testHard
- Question 42Vertical line testHard
- Question 43Vertical line testHard
- Question 44Vertical line testHard
- Question 45Vertical line testHard
- Question 46Parameter in a function relationHard
- Question 47Parameter in a function relationHard
- Question 48Parameter in a function relationHard
- Question 49Parameter in a function relationHard
- Question 50Parameter in a function relationHard