Relations and Functions Notes and Worksheets - Lindsay Bowden - Free Printable

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 relation that follows a strict rule — no input can be paired with more than one output. 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: In an ordered pair (x, y), 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: The x-column represents inputs; the y-column represents outputs. Each row is an ordered pair.)* | |
| MAPPING DIAGRAM | A type of diagram that shows the relationship between each input and output by using arrows. |  *(visual shown in worksheet)* |
| | *(Explanation: Left oval = inputs (domain); right oval = outputs (range). Arrows show which input maps to which output. For a function, no input can have more than one arrow.)* | |
| GRAPH | A visual display of ordered pairs. |  *(visual shown in worksheet)* |
| | *(Explanation: Points plotted on the coordinate plane represent the ordered pairs (x, y). If it passes the vertical line test — no vertical line crosses more than one point — then it’s a function.)* | |

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✔ Final Answer Summary (Filled Blanks):

- relation – A relationship between sets of values. The two types of values are called input and output.
- function – A special type of relation where each input has only one output.
- ORDERED PAIRS: The x coordinate and y coordinate of a point.
- X-Y TABLE: A table that shows inputs and outputs in terms of x and y.
- MAPPING DIAGRAM: A type of diagram that shows the relationship between each input and output by using arrows.
- GRAPH: A visual display of ordered pairs.

This completes the worksheet accurately and explains the key concepts behind relations and functions.