Card 1 of 20
EasyStudy card 1
Prompt
What is a relation?
It need not be a function.
Answer
A set of ordered pairs connecting inputs and outputs.
Example
\(\{(-1,4),(2,4)\}\) is a relation.
MathChapter 3: Functions and Linear Equations
Flashcards
Relations and Functions Flashcards
Twenty original recall cards covering 3-1 relations and functions concepts, procedures, graphs, and traps.
Current card1 / 20
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is the domain of a relation?
Read first coordinates.
Answer
The set of distinct input or x-values.
Example
For \((2,5),(4,5)\), the domain is \(\{2,4\}\).
Card 3 of 20
EasyStudy card 3
Prompt
What is the range of a relation?
Read second coordinates.
Answer
The set of distinct output or y-values.
Example
For \((2,5),(4,5)\), the range is \(\{5\}\).
Card 4 of 20
EasyStudy card 4
Prompt
What ordered-pair sign pattern identifies Quadrant II?
Move left, then up.
Answer
Negative x and positive y: \((-,+)\).
Example
\((-3,2)\) lies in Quadrant II.
Card 5 of 20
EasyStudy card 5
Prompt
Are points on an axis in a quadrant?
Quadrants are open regions.
Answer
No. Any point with x = 0 or y = 0 lies on an axis.
Example
\((0,-4)\) lies on the y-axis.
Card 6 of 20
MediumStudy card 6
Prompt
What condition makes a relation a function?
Count outputs per input.
Answer
Every input is associated with exactly one output.
Example
Different inputs may both map to \(7\).
Card 7 of 20
MediumStudy card 7
Prompt
What ordered-pair pattern proves a relation is not a function?
Repeated outputs are allowed.
Answer
The same input appears with two different outputs.
Example
\((3,1)\) and \((3,8)\) violate the rule.
Card 8 of 20
MediumStudy card 8
Prompt
How do you test a mapping for function status?
Ignore unused outputs.
Answer
Every input node must have exactly one outgoing arrow.
Example
Two arrows leaving one input fail the test.
Card 9 of 20
MediumStudy card 9
Prompt
State the vertical line test.
It counts outputs for fixed x.
Answer
A graph is a function of x if every vertical line intersects it at most once.
Example
A sideways parabola fails.
Card 10 of 20
MediumStudy card 10
Prompt
Why is a horizontal line a function of x?
Repeated outputs are permitted.
Answer
Each x-coordinate reaches the one constant y-value.
Example
\(y=4\) passes every vertical line test.
Card 11 of 20
MediumStudy card 11
Prompt
Why is a vertical line not y as a function of x?
It fails vertically.
Answer
One fixed x-value is paired with many y-values.
Example
\(x=2\) is a relation but not \(y=f(x)\).
Card 12 of 20
EasyStudy card 12
Prompt
What does f(x) mean?
It is function notation.
Answer
The output of function f at input x—not f multiplied by x.
Example
If \(f(x)=2x+1\), then \(f(3)=7\).
Card 13 of 20
MediumStudy card 13
Prompt
How do you evaluate f(-3)?
Protect negative signs.
Answer
Replace every x with parenthesized \((-3)\), then simplify.
Example
If \(f(x)=x^2\), \(f(-3)=9\).
Card 14 of 20
MediumStudy card 14
Prompt
How do you substitute a + 1 into a function?
Use parentheses everywhere.
Answer
Replace every x with \((a+1)\).
Example
\(f(a+1)=2(a+1)-5\) for \(f(x)=2x-5\).
Card 15 of 20
MediumStudy card 15
Prompt
Can two inputs share one output in a function?
Many-to-one is allowed.
Answer
Yes. The restriction is one output per input, not one input per output.
Example
\(f(-2)=f(2)=4\) for \(f(x)=x^2\).
Card 16 of 20
MediumStudy card 16
Prompt
Can a function table repeat an input?
Conflicting outputs fail.
Answer
Only if every occurrence of that input has the same output.
Example
Rows \((1,3)\) and \((1,3)\) do not conflict.
Card 17 of 20
MediumStudy card 17
Prompt
What representation makes function inputs and arrows especially visible?
Inputs and outputs appear in separate sets.
Answer
A mapping diagram.
Example
Inspect outgoing arrows, not incoming arrows.
Card 18 of 20
MediumStudy card 18
Prompt
What is the safest way to read an ordered pair?
x before y.
Answer
Horizontal x first, vertical y second.
Example
\((-4,2)\) means left 4 and up 2.
Card 19 of 20
MediumStudy card 19
Prompt
What is the key trap when listing range?
Use distinct y-values only.
Answer
Repeating an output or accidentally listing inputs.
Example
Outputs \(2,2,5\) give range \(\{2,5\}\).
Card 20 of 20
HardStudy card 20
Prompt
What must be true if (1,k) and (1,6) belong to a function?
The repeated input needs one output.
Answer
\(k=6\).
Example
Any other k gives input 1 conflicting outputs.
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