Here is the completed worksheet with all blanks filled in, along with explanations for each answer.
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RELATIONS & FUNCTIONS notes
relation - A
relationship between sets of values. The two types of values are called
input and
output.
> *Explanation:* A relation connects elements from one set (inputs) to another set (outputs). These are often called domain (inputs) and range (outputs).
function - A special type of
relation where each input has only
one output.
> *Explanation:* This is the key definition of a function — no input can map to more than one output. If it does, it’s a relation but not a function.
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WAYS TO REPRESENT RELATIONS
| WORD | DEFINITION | EXAMPLE |
|------------------|------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------|
|
ORDERED PAIRS | The
x coordinate and
y coordinate of a point. |
(x, y)<br>(1, 3), (2, 1), (3, 4), (5, 2) |
> *Explanation:* In an ordered pair (x, y), x is the horizontal (input) value and y is the vertical (output) value.
|
X-Y TABLE | A table that shows inputs and outputs in terms of
x and
y. | Table with columns labeled “x” and “y”, showing corresponding values. |
> *Explanation:* X-Y tables organize input-output pairs neatly, making it easy to see how x-values relate to y-values.
|
MAPPING DIAGRAM | A type of diagram that shows the relationship between each
input and
output by using arrows. | Diagram with two ovals: left = inputs (1,2,3,5), right = outputs (1,2,3,4), arrows connect them. |
> *Explanation:* Mapping diagrams visually link each input to its corresponding output(s). For a function, each input must have exactly one arrow.
|
GRAPH | A visual display of
ordered pairs (or a relation/function). | Coordinate plane with plotted points connected by lines or dots. |
> *Explanation:* Graphs plot ordered pairs on the x-y plane. If you can pass the vertical line test (no vertical line crosses more than one point), it represents a function.
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✔ All blanks filled correctly based on standard math definitions for relations and functions.
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