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 labeled as x-values (input) and y-values (output).)*
function – A special type of
relation where each input has only
one output.
*(Explanation: A function is a stricter kind of relation — for every input value, there must be exactly one corresponding output value. This is the “vertical line test” rule in graphs.)*
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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: Ordered pairs are written as (x, y), where x is the horizontal position and y is the vertical position on a coordinate plane.)* | |
|
X-Y TABLE | A table that shows inputs and outputs in terms of
x and
y. | <table><tr><th>x</th><th>y</th></tr><tr><td>1</td><td>3</td></tr><tr><td>2</td><td>1</td></tr><tr><td>3</td><td>4</td></tr><tr><td>5</td><td>2</td></tr></table> |
| | *(Explanation: An x-y table organizes data into columns — x represents the input, y represents the output. Each row is an ordered pair.)* | |
|
MAPPING DIAGRAM | A type of diagram that shows the relationship between each
input and
output by using arrows. | <br>Input: {1,2,3,5} → Output: {1,2,3,4} with arrows connecting them. |
| | *(Explanation: Mapping diagrams visually link each element in the input set to its corresponding output using arrows. In this example, each input maps to exactly one output, so it’s also a function.)* | |
|
GRAPH | A visual display of
ordered pairs. | <br>A coordinate plane with plotted points connected by lines. |
| | *(Explanation: A graph plots the ordered pairs (x, y) on a coordinate plane. If you can draw a vertical line anywhere and it crosses the graph at most once, then it represents a function.)* | |
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✔ Final Answer Summary (Filled Blanks):
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relation: relationship; input; output
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function: relation; one
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Ordered Pairs: x; y
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X-Y Table: x; y
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Mapping Diagram: input; output
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Graph: ordered pairs
This worksheet teaches the foundational concepts of relations and functions, and how they can be represented in multiple ways — which is essential for understanding algebra and graphing!
© Lindsay Bowden, 2020
Parent Tip: Review the logic above to help your child master the concept of identifying relations and functions worksheet.
